A fast block low-rank dense solver with applications to finite-element matrices
This article presents a fast solver for the dense “frontal” matrices that arise from the
multifrontal sparse elimination process of 3D elliptic PDEs. The solver relies on the fact that …
multifrontal sparse elimination process of 3D elliptic PDEs. The solver relies on the fact that …
An immersed boundary method for rigid bodies
We develop an immersed boundary (IB) method for modeling flows around fixed or moving
rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes …
rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes …
The inverse fast multipole method: using a fast approximate direct solver as a preconditioner for dense linear systems
Although some preconditioners are available for solving dense linear systems, there are still
many matrices for which preconditioners are lacking, particularly in cases where the size of …
many matrices for which preconditioners are lacking, particularly in cases where the size of …
Immersed boundary smooth extension: a high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods
Abstract The Immersed Boundary method is a simple, efficient, and robust numerical
scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy …
scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy …
[BOOK][B] Fast direct solvers for elliptic PDEs
PG Martinsson - 2019 - SIAM
In writing this book, I set out to create an accessible introduction to fast multipole methods
(FMMs) and techniques based on integral equation formulations. These are powerful tools …
(FMMs) and techniques based on integral equation formulations. These are powerful tools …
Fast hierarchical solvers for sparse matrices using extended sparsification and low-rank approximation
Inversion of sparse matrices with standard direct solve schemes is robust but
computationally expensive. Iterative solvers, on the other hand, demonstrate better …
computationally expensive. Iterative solvers, on the other hand, demonstrate better …
Accuracy Directly Controlled Fast Direct Solution of General -Matrices and Its Application to Solving Electrodynamic Volume Integral Equations
The dense matrix resulting from an integral equation (IE)-based solution of Maxwell's
equations can be compactly represented by an H 2-matrix. Given a general dense H 2 …
equations can be compactly represented by an H 2-matrix. Given a general dense H 2 …
Solving linear systems on a GPU with hierarchically off-diagonal low-rank approximations
We are interested in solving linear systems arising from three applications:(1) kernel
methods in machine learning,(2) discretization of boundary integral equations from …
methods in machine learning,(2) discretization of boundary integral equations from …
Extreme scale FMM-accelerated boundary integral equation solver for wave scattering
We present a boundary integral equation solver for wave scattering suited for many-core
processors, which are expected to be the building blocks of energy-austere exascale …
processors, which are expected to be the building blocks of energy-austere exascale …
A tensor-train accelerated solver for integral equations in complex geometries
We present a framework using the Quantized Tensor Train (qtt) decomposition to accurately
and efficiently solve volume and boundary integral equations in three dimensions. We …
and efficiently solve volume and boundary integral equations in three dimensions. We …