@article{https://authors.library.caltech.edu/records/ca73j-gkv41, title = "Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes", journal = "Nonlinearity", year = "2024", url = "https://authors.library.caltech.edu/records/ca73j-gkv41", id = "record", issn = "0951-7715", doi = "10.1088/1361-6544/ad1c2f", volume = "37" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230515-138520000.12, title = "Exponentially Convergent Multiscale Finite Element Method", journal = "Communications on Applied Mathematics and Computation", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230515-138520000.12", id = "record", issn = "2096-6385", doi = "10.1007/s42967-023-00260-2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230530-441187700.9, title = "Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients", journal = "Multiscale Modeling and Simulation", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230530-441187700.9", id = "record", issn = "1540-3459", doi = "10.1137/22m1470906", volume = "21" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-194424192, title = "Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-194424192", id = "record", doi = "10.48550/arXiv.2212.11912" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-192413744, title = "Potential singularity of the 3D Euler equations in the interior domain", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-192413744", id = "record", doi = "10.48550/arXiv.2107.05870" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-194417020, title = "On stability and instability of C^(1,α) singular solutions to the 3D Euler and 2D Boussinesq equations", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-194417020", id = "record", doi = "10.48550/arXiv.2206.01296" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-193545252, title = "The potentially singular behavior of the 3D Navier-Stokes equations", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-193545252", id = "record", doi = "10.48550/arXiv.2107.06509" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-194420642, title = "Exponentially Convergent Multiscale Finite Element Method", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-194420642", id = "record", doi = "10.48550/arXiv.2212.00823" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-191437852, title = "Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-191437852", id = "record", doi = "10.48550/arXiv.2210.07191" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20230227-194427740, title = "Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part II: the N-Dimensional Case", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-194427740", id = "record", doi = "10.48550/arXiv.2212.11924" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20221221-220346410, title = "Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221221-220346410", id = "record", doi = "10.48550/arXiv.2107.09207" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20221221-220354531, title = "Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221221-220354531", id = "record", doi = "10.48550/arXiv.2012.15467" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20221221-004750416, title = "Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221221-004750416", id = "record", doi = "10.48550/arXiv.2211.15960" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20220919-258327700, title = "Potentially Singular Behavior of the 3D Navier-Stokes Equations", journal = "Foundations of Computational Mathematics", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220919-258327700", id = "record", issn = "1615-3375", doi = "10.1007/s10208-022-09578-4" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20220919-922490500, title = "Potential Singularity of the 3D Euler Equations in the Interior Domain", journal = "Foundations of Computational Mathematics", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220919-922490500", id = "record", issn = "1615-3375", doi = "10.1007/s10208-022-09585-5" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20220607-425321000, title = "A potential two-scale traveling wave singularity for 3D incompressible Euler equations", journal = "Physica D", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220607-425321000", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2022.133257", volume = "435" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20221128-494241100.17, title = "Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations", journal = "Annals of PDE", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221128-494241100.17", id = "record", issn = "2524-5317", doi = "10.1007/s40818-022-00140-7", volume = "8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20220801-490095000, title = "Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data", journal = "Multiscale Modeling and Simulation", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220801-490095000", id = "record", issn = "1540-3459", doi = "10.1137/20m1372214", volume = "20" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20220622-203755587, title = "Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference", journal = "Proceedings of Machine Learning Research", year = "2021", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220622-203755587", id = "record", issn = "2640-3498", doi = "10.48550/arXiv.2105.05489", volume = "139" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20210922-170252834, title = "Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions", journal = "Multiscale Modeling and Simulation", year = "2021", url = "https://resolver.caltech.edu/CaltechAUTHORS:20210922-170252834", id = "record", issn = "1540-3459", doi = "10.1137/20m1352922", volume = "19" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200123-101534089, title = "On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations", journal = "Communications on Pure and Applied Mathematics", year = "2021", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200123-101534089", id = "record", issn = "0010-3640", doi = "10.1002/cpa.21991", volume = "74" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200122-142818756, title = "Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^(1,α) Velocity and Boundary", journal = "Communications in Mathematical Physics", year = "2021", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-142818756", id = "record", issn = "0010-3616", doi = "10.1007/s00220-021-04067-1", volume = "383" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200122-075925100, title = "Function approximation via the subsampled Poincaré inequality", journal = "Discrete and Continuous Dynamical Systems - Series A", year = "2021", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-075925100", id = "record", issn = "1553-5231", doi = "10.3934/dcds.2020296", volume = "41" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200124-145020991, title = "A prototype knockoff filter for group selection with FDR control", journal = "Information and Inference", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200124-145020991", id = "record", issn = "2049-8772", doi = "10.1093/imaiai/iaz012", volume = "9" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200123-103312153, title = "A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates", journal = "Journal of the Royal Society Interface", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200123-103312153", id = "record", issn = "1742-5689", doi = "10.1098/rsif.2020.0175", volume = "17", pmcid = "PMC7276546" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20200122-143531561, title = "A class of robust numerical methods for solving dynamical systems with multiple time scales", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-143531561", id = "record", doi = "10.48550/arXiv.1909.04289" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20200122-133158689, title = "Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-133158689", id = "record", doi = "10.48550/arXiv.1911.12518" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20191202-133631090, title = "Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study", journal = "SIAM Review", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20191202-133631090", id = "record", issn = "0036-1445", doi = "10.1137/19m1288061", volume = "61" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190620-093003600, title = "Solving Bayesian inverse problems from the perspective of deep generative networks", journal = "Computational Mechanics", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190620-093003600", id = "record", issn = "0178-7675", doi = "10.1007/s00466-019-01739-7", volume = "64" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190711-100817562, title = "A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach", journal = "Multiscale Modeling and Simulation", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190711-100817562", id = "record", issn = "1540-3459", doi = "10.1137/18m1205844", volume = "17" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20191114-104110525, title = "A pseudo knockoff filter for correlated features", journal = "Information and Inference", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20191114-104110525", id = "record", issn = "2049-8772", doi = "10.1093/imaiai/iay012", volume = "8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190416-073721627, title = "A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition", journal = "Multiscale Modeling and Simulation", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190416-073721627", id = "record", issn = "1540-3459", doi = "10.1137/18m1180827", volume = "17" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170306-105506989, title = "Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow", journal = "Journal of Nonlinear Science", year = "2018", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170306-105506989", id = "record", issn = "0938-8974", doi = "10.1007/s00332-017-9370-9", volume = "28" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20180405-130644881, title = "Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations", journal = "Nonlinearity", year = "2018", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180405-130644881", id = "record", issn = "0951-7715", doi = "10.1088/1361-6544/aaaa0b", volume = "31" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20180718-150855095, title = "An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition", journal = "Multiscale Modeling and Simulation", year = "2018", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180718-150855095", id = "record", issn = "1540-3459", doi = "10.1137/17M1140686", volume = "16" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20171205-123956892, title = "Sparse operator compression of higher-order elliptic operators with rough coefficients", journal = "Research in the Mathematical Sciences", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20171205-123956892", id = "record", issn = "2197-9847", doi = "10.1186/s40687-017-0113-1", volume = "4" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170509-075902405, title = "On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations", journal = "Communications on Pure and Applied Mathematics", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170509-075902405", id = "record", issn = "0010-3640", doi = "10.1002/cpa.21697", volume = "70" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170719-100127267, title = "A two-level method for sparse time-frequency representation of multiscale data", journal = "Science China Mathematics", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170719-100127267", id = "record", issn = "1674-7283", doi = "10.1007/s11425-016-9088-9", volume = "60" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170427-144329075, title = "An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients", journal = "Journal of Computational Physics", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170427-144329075", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2017.02.002", volume = "336" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170413-142311390, title = "Exploring the locally low dimensional structure in solving random elliptic PDEs", journal = "Multiscale Modeling \& Simulation", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170413-142311390", id = "record", issn = "1540-3459", doi = "10.1137/16M1077611", volume = "15" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170413-141136299, title = "A sparse decomposition of low rank symmetric positive semi-definite matrices", journal = "Multiscale Modeling and Simulation", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170413-141136299", id = "record", issn = "1540-3459", doi = "10.1137/16M107760X", volume = "15" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170214-074909079, title = "Identification of time-varying cable tension forces based on adaptive sparse time-frequency analysis of cable vibrations", journal = "Structural Control and Health Monitoring", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170214-074909079", id = "record", issn = "1545-2255", doi = "10.1002/stc.1889", volume = "24" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161103-105632603, title = "An Accelerated Method for Nonlinear Elliptic PDE", journal = "Journal of Scientific Computing", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161103-105632603", id = "record", issn = "0885-7474", doi = "10.1007/s10915-016-0215-8", volume = "69" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160624-151830832, title = "Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods", journal = "Journal of Computational Physics", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160624-151830832", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2016.04.054", volume = "320" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160315-134934235, title = "Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient", journal = "Discrete and Continuous Dynamical Systems", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-134934235", id = "record", issn = "1078-0947", doi = "10.3934/dcds.2016.36.4451", volume = "36" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160322-071936317, title = "Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-071936317", id = "record", doi = "10.48550/arXiv.0601427" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160315-133921211, title = "Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-133921211", id = "record", doi = "10.48550/arXiv.1407.5740" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160315-123826115, title = "On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-123826115", id = "record", doi = "10.48550/arXiv.1407.4776" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160315-134409579, title = "On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-134409579", id = "record", doi = "10.48550/arXiv.1311.2613" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160315-152129723, title = "Sparse Time-Frequency decomposition for multiple signals with same frequencies", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-152129723", id = "record", doi = "10.48550/arXiv.1507.02037" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160315-133702384, title = "On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-133702384", id = "record", doi = "10.48550/arXiv.1107.1823" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160315-092552095, title = "Adaptive data analysis: theory and applications", journal = "Philosophical Transactions A: Mathematical, Physical and Engineering Sciences", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-092552095", id = "record", issn = "1364-503X", doi = "10.1098/rsta.2015.0207", volume = "374" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160315-095503958, title = "Sparse time-frequency decomposition based on dictionary adaptation", journal = "Philosophical Transactions A: Mathematical, Physical and Engineering Sciences", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-095503958", id = "record", issn = "1364-503X", doi = "10.1098/rsta.2015.0192", volume = "374", pmcid = "PMC4792402" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160315-095910709, title = "Extracting a shape function for a signal with intra-wave frequency modulation", journal = "Philosophical Transactions A: Mathematical, Physical and Engineering Sciences", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-095910709", id = "record", issn = "1364-503X", doi = "10.1098/rsta.2015.0194", volume = "374", pmcid = "PMC4792404" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161014-130127343, title = "A Model Reduction Method for Elliptic PDEs with Random Input Using the Heterogeneous Stochastic FEM Framework", journal = "Bulletin of the Intitute of Mathematics Academia Sinica", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161014-130127343", id = "record", issn = "2304-7909", volume = "11" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170621-112302718, title = "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", chapter = "Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170621-112302718", id = "record", isbn = "978-3-319-10151-4", doi = "10.1007/978-3-319-10151-4\_17-1" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160404-090937429, title = "On the convergence and accuracy of the cardiovascular intrinsic frequency method", journal = "Royal Society Open Science", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160404-090937429", id = "record", issn = "2054-5703", doi = "10.1098/rsos.150475", volume = "2", pmcid = "PMC4807454" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20151023-103928257, title = "On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data", journal = "Multiscale Modeling and Simulation", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20151023-103928257", id = "record", issn = "1540-3459", doi = "10.1137/141002098", volume = "13" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20150501-105112539, title = "A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients", journal = "Multiscale Modeling and Simulation", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150501-105112539", id = "record", issn = "1540-3459", doi = "10.1137/130948136", volume = "13" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20150115-154548810, title = "A heterogeneous stochastic FEM framework for elliptic PDEs", journal = "Journal of Computational Physics", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150115-154548810", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2014.10.020", volume = "281" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20150519-083002339, title = "Sparse Time Frequency Representations and Dynamical Systems", journal = "Communications in Mathematical Sciences", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150519-083002339", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2015.v13.n3.a4", volume = "13" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20150202-093859868, title = "Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method", journal = "Multiscale Modeling and Simulation", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150202-093859868", id = "record", issn = "1540-3459", doi = "10.1137/140957767", volume = "12" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140825-230506377, title = "Potentially singular solutions of the 3D axisymmetric Euler equations", journal = "Proceedings of the National Academy of Sciences of the United States of America", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140825-230506377", id = "record", issn = "0027-8424", doi = "10.1073/pnas.1405238111", volume = "111", pmcid = "PMC4246962" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140825-134136758, title = "Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications", journal = "Journal of the Royal Society Interface", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140825-134136758", id = "record", issn = "1742-5689", doi = "10.1098/rsif.2014.0617", volume = "11", pmcid = "PMC4233710" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20150112-104708436, title = "Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient", journal = "Communications in Computational Physics", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150112-104708436", id = "record", issn = "1815-2406", doi = "10.4208/cicp.270913.020414a", volume = "16" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140731-103641810, title = "Convergence of a data-driven time–frequency analysis method", journal = "Applied and Computational Harmonic Analysis", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140731-103641810", id = "record", issn = "1063-5203", doi = "10.1016/j.acha.2013.12.004", volume = "37" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140422-134241808, title = "On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations", journal = "Archive for Rational Mechanics and Analysis", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140422-134241808", id = "record", issn = "0003-9527", doi = "10.1007/s00205-013-0717-6", volume = "212" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20150202-082208889, title = "Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation", journal = "Multiscale Modeling \& Simulation", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150202-082208889", id = "record", issn = "1540-3459", doi = "10.1137/140966411", volume = "12" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140407-110251743, title = "A Multiscale Model Reduction Method for Partial Differential Equations", journal = "ESAIM-Mathematical Modelling and Numerical Analysis", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140407-110251743", id = "record", issn = "0764-583X", doi = "10.1051/m2an/2013115", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140113-074436396, title = "Sparse time-frequency representation of nonlinear and nonstationary data", journal = "Science China Mathematics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140113-074436396", id = "record", issn = "1674-7283", doi = "10.1007/s11425-013-4733-7", volume = "56" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130830-131942975, title = "Generalized multiscale finite element methods (GMsFEM)", journal = "Journal of Computational Physics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130830-131942975", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2013.04.045", volume = "251" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130725-100732399, title = "Data-driven time–frequency analysis", journal = "Applied and Computational Harmonic Analysis", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130725-100732399", id = "record", issn = "1063-5203", doi = "10.1016/j.acha.2012.10.001", volume = "35" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20140822-131136037, title = "A decadal microwave record of tropical air temperature from AMSU-A/aqua observations", journal = "Climate Dynamics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140822-131136037", id = "record", issn = "0930-7575", doi = "10.1007/s00382-013-1696-x", volume = "41" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130702-134527463, title = "A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms", journal = "Journal of Computational Physics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130702-134527463", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2013.02.033", volume = "242" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130701-154101667, title = "A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations", journal = "Journal of Computational Physics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130701-154101667", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2013.02.020", volume = "242" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130104-102700776, title = "Multiscale modeling of incompressible turbulent flows", journal = "Journal of Computational Physics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130104-102700776", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2012.08.029", volume = "232" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130305-095227632, title = "Numerical simulation of water resources problems: Models, methods, and trends", journal = "Advances in Water Resources", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130305-095227632", id = "record", issn = "0309-1708", doi = "10.1016/j.advwatres.2012.05.008", volume = "51" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120523-112912673, title = "On singularity formation of a 3D model for incompressible Navier–Stokes equations", journal = "Advances in Mathematics", year = "2012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120523-112912673", id = "record", issn = "0001-8708", doi = "10.1016/j.aim.2012.02.015", volume = "230" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120326-132813054, title = "Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model", journal = "Discrete and Continuous Dynamical Systems", year = "2012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120326-132813054", id = "record", issn = "1078-0947", doi = "10.3934/dcds.2012.32.1449", volume = "32" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20200203-134704241, title = "Numerical Analysis of Multiscale Problems", year = "2012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200203-134704241", id = "record", isbn = "978-3-642-22060-9", doi = "10.1007/978-3-642-22061-6" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20180904-093329630, title = "Introduction", journal = "Advances in Adaptive Data Analysis", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180904-093329630", id = "record", issn = "1793-5369", doi = "10.1142/S1793536911000672", volume = "3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120314-131024684, title = "Adaptive data analysis via sparse time-frequency representation", journal = "Advances in Adaptive Data Analysis", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120314-131024684", id = "record", issn = "1793-5369", doi = "10.1142/S1793536911000647", volume = "3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110228-113453092, title = "On Singularity Formation of a Nonlinear Nonlocal System", journal = "Archive for Rational Mechanics and Analysis", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110228-113453092", id = "record", issn = "0003-9527", doi = "10.1007/s00205-010-0319-5", volume = "199" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120322-080850518, title = "Introduction", journal = "Advances in Adaptive Data Analysis", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120322-080850518", id = "record", issn = "1793-5369", doi = "10.1142/S1793536911000672", volume = "3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20101012-100934632, title = "A new multiscale finite element method for high-contrast elliptic interface problems", journal = "Mathematics of Computation", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20101012-100934632", id = "record", issn = "0025-5718", volume = "79" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20180808-083855888, title = "Nonlinear Conservation Laws, Fluid Systems and Related Topics", chapter = "Introduction to the Theory of Incompressible Inviscid Flows", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180808-083855888", id = "record", isbn = "978-981-4273-27-5", doi = "10.1142/9789814273282\_0001" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20180808-083034185, title = "Multi-Scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulation", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180808-083034185", id = "record", isbn = "978-981-4273-25-1", doi = "10.1142/7291" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20090624-105309162, title = "On the Partial Regularity of a 3D Model of the Navier-Stokes Equations", journal = "Communications in Mathematical Physics", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090624-105309162", id = "record", issn = "0010-3616", doi = "10.1007/s00220-008-0689-9", volume = "287" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20090528-090507806, title = "On the stabilizing effect of convection in three-dimensional incompressible flows", journal = "Communications on Pure and Applied Mathematics", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090528-090507806", id = "record", issn = "0010-3640", doi = "10.1002/cpa.20254", volume = "62" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUdcds09, title = "Multiscale analysis for convection dominated transport equations", journal = "Discrete and Continuous Dynamical Systems", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUdcds09", id = "record", issn = "1078-0947", doi = "10.3934/dcds.2009.23.281", volume = "23" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20180810-134356708, title = "Multiscale Finite Element Methods: Theory and Applications", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180810-134356708", id = "record", isbn = "978-0-387-09495-3", doi = "10.1007/978-0-387-09496-0" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20100622-112319775, title = "Multiscale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations", chapter = "Multiscale computations for flow and transport in porous media", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100622-112319775", id = "record", isbn = "9789814273268" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110321-155230291, title = "Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations", journal = "Acta Numerica", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110321-155230291", id = "record", issn = "0962-4929", doi = "10.1017/S0962492906420018", volume = "18" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20090819-164116745, title = "Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries", journal = "Journal of Computational Mathematics", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090819-164116745", id = "record", issn = "0254-9409", doi = "10.4208/jcm.2009.27.4.012", volume = "27" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08b, title = "Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations", journal = "Journal of Computational Physics", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08b", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2008.03.002", volume = "227" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08a, title = "An efficient semi-implicit immersed boundary method for the Navier–Stokes equations", journal = "Journal of Computational Physics", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08a", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2008.07.005", volume = "227" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20091014-100827184, title = "Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data", journal = "Communications in Partial Differential Equation", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:20091014-100827184", id = "record", issn = "0360-5302", doi = "10.1080/03605300802108057", volume = "33" } @article{https://resolver.caltech.edu/CaltechAUTHORS:EFEcg08, title = "Multiscale simulations of porous media flows in flow-based coordinate system", journal = "Computational Geosciences", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFEcg08", id = "record", issn = "1420-0597", doi = "10.1007/s10596-007-9073-7", volume = "12" } @article{https://resolver.caltech.edu/CaltechAUTHORS:DOScmame08, title = "Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification", journal = "Computer Methods in Applied Mechanics and Engineering", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:DOScmame08", id = "record", issn = "0045-7825", doi = "10.1016/j.cma.2008.02.030", volume = "197" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:EFElnm08, title = "Quantum Treansport: Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11–16, 2006", chapter = "Multiscale Computations for Flow and Transport in Heterogeneous Media", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFElnm08", id = "record", isbn = "978-3-540-79573-5", doi = "10.1007/978-3-540-79574-2\_4" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160322-093035560, title = "Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl", journal = "Communications on Pure and Applied Mathematics", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-093035560", id = "record", issn = "0010-3640", doi = "10.1002/cpa.20212", volume = "61" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUmms08, title = "Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations", journal = "Multiscale Modeling and Simulation", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUmms08", id = "record", issn = "1540-3459", doi = "10.1137/070682046", volume = "6" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20200127-092428769, title = "Mathematics and Computation, a Contemporary View", chapter = "Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200127-092428769", id = "record", isbn = "978-3-540-68848-8", doi = "10.1007/978-3-540-68850-1\_3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160322-083351617, title = "Computing nearly singular solutions using pseudo-spectral methods", journal = "Journal of Computational Physics", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-083351617", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2007.04.014", volume = "226" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200310-145803950, title = "Mathematical modeling and simulation of aquatic and aerial animal locomotion", journal = "Journal of Computational Physics", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200310-145803950", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2007.02.015", volume = "225" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160322-091323469, title = "Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations", journal = "Discrete and Continuous Dynamical Systems", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-091323469", id = "record", issn = "1078-0947", doi = "10.3934/dcds.2007.18.637", volume = "18" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20100826-114814124, title = "Multiscale finite element methods for porous media flows and their applications", journal = "Applied Numerical Mathematics", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100826-114814124", id = "record", issn = "0168-9274", doi = "10.1016/j.apnum.2006.07.009", volume = "57" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUpnas07, title = "Organized structures, memory, and the decay of turbulence", journal = "Proceedings of the National Academy of Sciences of the United States of America", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUpnas07", id = "record", issn = "0027-8424", doi = "10.1073/pnas.0700639104", volume = "104", pmcid = "PMC1871813" } @article{https://resolver.caltech.edu/CaltechAUTHORS:TANcpl07, title = "Bridging Atomistic/Continuum Scales in Solids with Moving Dislocations", journal = "Chinese Physics Letters", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:TANcpl07", id = "record", issn = "0256-307X", doi = "10.1088/0256-307X/24/1/044", volume = "24" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20190820-155926497, title = "Computational Mechanics", chapter = "A Relay-Zone Technique for Computing Dynamic Dislocations", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190820-155926497", id = "record", isbn = "978-3-540-75998-0", doi = "10.1007/978-3-540-75999-7\_28" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUmms06, title = "A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media", journal = "Multiscale Modeling \& Simulation", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUmms06", id = "record", issn = "1540-3459", doi = "10.1137/050646020", volume = "5" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160322-090700507, title = "Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations", journal = "Journal of Nonlinear Science", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-090700507", id = "record", issn = "0938-8974", doi = "10.1007/s00332-006-0800-3", volume = "16" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjma06, title = "On Global Well-Posedness of the Lagrangian Averaged Euler Equations", journal = "SIAM Journal on Mathematical Analysis", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjma06", id = "record", issn = "0036-1410", doi = "10.1137/050625783", volume = "38" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUccp06, title = "A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate", journal = "Communications in Computational Physics", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUccp06", id = "record", issn = "1815-2406", volume = "1" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409, title = "Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation", journal = "Communications in Partial Differential Equations", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409", id = "record", issn = "0360-5302", doi = "10.1080/03605300500358152", volume = "31" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20110602-094821767, title = "Inverse problems, multi-scale analysis, and effective medium theory", chapter = "Multiscale computation of isotropic homogeneous turbulent flow", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110602-094821767", id = "record", isbn = "0-8218-3968-3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:EFEsiamjsc06, title = "Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models", journal = "SIAM Journal on Scientific Computing", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFEsiamjsc06", id = "record", issn = "1064-8275", doi = "10.1137/050628568", volume = "28" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170408-161459048, title = "Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation", journal = "Discrete and Continuous Dynamical Systems", year = "2005", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170408-161459048", id = "record", issn = "1078-0947", doi = "10.3934/dcds.2005.13.1153", volume = "13" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20180404-083725024, title = "Multiscale modelling and computation of fluid flow", journal = "International Journal for Numerical Methods in Fluids", year = "2005", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180404-083725024", id = "record", issn = "0271-2091", doi = "10.1002/fld.866", volume = "47" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160322-075428588, title = "Geometric Properties and Nonblowup of 3D Incompressible Euler Flow", journal = "Communications in Partial Differential Equations", year = "2005", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-075428588", id = "record", issn = "0360-5302", doi = "10.1081/PDE-200044488", volume = "30" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630, title = "Multiscale Finite Element Methods for Nonlinear Problems and their Applications", journal = "Communications in Mathematical Sciences", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630", id = "record", issn = "1539-6746", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20111013-071805594, title = "A modified particle method for semilinear hyperbolic systems with oscillatory solutions", journal = "Methods and Applications of Analysis", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111013-071805594", id = "record", issn = "1073-2772", volume = "11" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20111014-070953819, title = "Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation", journal = "Communications in Mathematical Sciences", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111014-070953819", id = "record", issn = "1539-6746", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110819-082640450, title = "Homogenization of incompressible Euler equations", journal = "Journal of Computational Mathematics", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110819-082640450", id = "record", issn = "0254-9409", volume = "22" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUpof03, title = "Singularity formation in three-dimensional vortex sheets", journal = "Physics of Fluids", year = "2003", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUpof03", id = "record", issn = "1070-6631", doi = "10.1063/1.1526100", volume = "15" } @article{https://resolver.caltech.edu/CaltechAUTHORS:CHEmc03, title = "A mixed multiscale finite element method for elliptic problems with oscillating coefficients", journal = "Mathematics of Computation", year = "2002", url = "https://resolver.caltech.edu/CaltechAUTHORS:CHEmc03", id = "record", issn = "0025-5718", volume = "72" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446, title = "Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios", journal = "Acta Mathematicae Applicatae Sinica, English Series", year = "2002", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446", id = "record", issn = "0168-9673", doi = "10.1007/s102550200004", volume = "18" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20200226-133732456, title = "Advances in Applied Mechanics", chapter = "Coastal hydrodynamics of ocean waves on beach", year = "2001", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200226-133732456", id = "record", isbn = "9780120020379", doi = "10.1016/s0065-2156(00)80005-8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:CENjfm00, title = "The singular perturbation of surface tension in Hele-Shaw flows", journal = "Journal of Fluid Mechanics", year = "2000", url = "https://resolver.caltech.edu/CaltechAUTHORS:CENjfm00", id = "record", issn = "0022-1120", doi = "10.1017/S0022112099007703", volume = "409" } @article{https://resolver.caltech.edu/CaltechAUTHORS:EFEsiam00, title = "Convergence of a nonconforming multiscale finite element method", journal = "SIAM Journal on Numerical Analysis", year = "2000", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFEsiam00", id = "record", issn = "0036-1429", doi = "10.1137/S0036142997330329", volume = "37" } @article{https://resolver.caltech.edu/CaltechAUTHORS:CENpof99, title = "Numerical study of Hele-Shaw flow with suction", journal = "Physics of Fluids", year = "1999", url = "https://resolver.caltech.edu/CaltechAUTHORS:CENpof99", id = "record", issn = "1070-6631", doi = "10.1063/1.870112", volume = "11" } @article{https://resolver.caltech.edu/CaltechAUTHORS:CENpof99a, title = "Dynamic generation of capillary waves", journal = "Physics of Fluids", year = "1999", url = "https://resolver.caltech.edu/CaltechAUTHORS:CENpof99a", id = "record", issn = "1070-6631", doi = "10.1063/1.869975", volume = "11" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUpre98, title = "Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces", journal = "Physical Review E", year = "1998", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUpre98", id = "record", issn = "1063-651X", doi = "10.1103/PhysRevE.58.5841", volume = "58" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUdmicm98, title = "Numerical Study of Free Interface Problems Using Boundary Integral Methods", journal = "Documenta Mathematica", year = "1998", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUdmicm98", id = "record", issn = "1431-0635", volume = "Extra" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170707-134035089, title = "A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media", journal = "Journal of Computational Physics", year = "1997", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170707-134035089", id = "record", issn = "0021-9991", doi = "10.1006/jcph.1997.5682", volume = "134" } @article{https://resolver.caltech.edu/CaltechAUTHORS:BEAsiamjna96, title = "Convergence of a Boundary Integral Method for Water Waves", journal = "SIAM Journal on Numerical Analysis", year = "1996", url = "https://resolver.caltech.edu/CaltechAUTHORS:BEAsiamjna96", id = "record", issn = "0036-1429", doi = "10.1137/S0036142993245750", volume = "33" } @article{https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjna93, title = "Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries", journal = "SIAM Journal on Numerical Analysis", year = "1993", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjna93", id = "record", issn = "0036-1429", doi = "10.1137/0730030", volume = "30" }