We develop a method for numerical time-domain wave propagation based on the model order reduction approach. The method is built with high-performance computing (HPC) implementation in mind that implies a high level of parallelism and greatly reduced communication requirements compared to the traditional high-order finite-difference time-domain (FDTD) methods. The approach is inherently multiscale, with a reference fine grid model being split into subdomains. For each subdomain the coarse scale reduced order models (ROMs) are precomputed off-line in a parallel manner. The ROMs approximate the Neumann-to-Dirichlet (NtD) maps with high (spectral) accuracy and are used to couple the adjacent subdomains on the shared boundaries. The on-line part of the method is an explicit time stepping with the coupled ROMs. To lower the on-line computation cost the reduced order spatial operator is sparsified by transforming to a matrix Stieltjes continued fraction (S-fraction) form. The on-line communication costs are also reduced due to the ROM NtD map approximation properties. Another source of performance improvement is the time step length. Properly chosen ROMs substantially improve the Courant-Friedrichs-Lewy (CFL) condition. This allows the CFL time step to approach the Nyquist limit, which is typically unattainable with traditional schemes that have the CFL time step much smaller than the Nyquist sampling rate.
Fourier series (based) multiscale method for computational analysis in science and engineering: VI. Fourier series multiscale solution for wave propagation in a beam with rectangular cross section
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the sixth paper, exact analysis of the wave propagation in a beam with rectangular cross section is extended to a thorough multiscale analysis for a system of completely coupled second order linear differential equations for modal functions, where general boundary conditions are prescribed. For this purpose, the modal function each is expressed as a linear combination of the corner function, the two boundary functions and the internal func…
Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media
Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media
Texas A&M University（德克萨斯农工大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Chinese University of Hong Kong（香港中文大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Multiscale Methods for wave propagation in materials with sign-changing coefficients
The Chinese University of Hong Kong（香港中文大学）；POEMS, CNRS, INRIA, ENSTA Paris, Institut Polytechnique de Paris（巴黎理工学院）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）
Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation
National Center for Applied Mathematics（应用数学国家研究中心）；Tianjin University（天津大学）；School of Mechanical and Aerospace Engineering, Jilin University（吉林大学机械与航空航天工程学院）；Jilin University（吉林大学）
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime
National University of Singapore（新加坡国立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Purdue University（普渡大学）；Université de Lorraine（洛林大学）；Inria Nancy-Grand Est（南锡大东部国家研究学院）
