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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs
HT-Net 分层变压器 多尺度 偏微分方程 算子学习模型
2023/5/6
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...
Fast construction of hierarchical matrix representation from matrix–vector multiplication
Fast algorithm Hierarchical matrix construction Randomized singular value decomposition Matrix–vector multiplication Elliptic operator Green’s function
2015/7/14
We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses Oelog nT appl...
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Elliptic equations Fast algorithms Nested dissection Hierarchical matrices Sparse matrix
2015/7/14
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining...
Hierarchical Interpolative Factorization for Elliptic Operators:Integral Equations
Hierarchical Interpolative Factorization Elliptic Operators Integral Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
Hierarchical Interpolative Factorization for Elliptic Operators:Differential Equations
Hierarchical Interpolative Factorization Elliptic Operators Differential Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an a...