79 citations · 95 across the 26 of their papers we have counts for
9 papers · 1 filter
A performance portable fast Ewald summation for Stokes flow
Gabriel Kosmacher, Ziyu Du, Joar Bagge +1
We present GPU algorithms for Ewald summation methods for accelerating N-body Stokes flow problems in periodic domains. Like most N-body codes, Ewald sums use a near-field/far-fiel…
IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients
Shan Zhong, George Biros
We introduce a novel neural operator architecture designed to approximate solutions of linear elliptic partial differential equations with high-contrast, spatially varying coeffici…
Inverse Problem Regularization for 3D Multi-Species Tumor Growth Models
Ali Ghafouri, George Biros
We present a multi-species partial differential equation (PDE) model for tumor growth and a an algorithm for calibrating the model from magnetic resonance imaging (MRI) scans. The…
An O(N) distributed-memory parallel direct solver for planar integral equations
Tianyu Liang, Chao Chen, Per-Gunnar Martinsson +1
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be al…
Numerical simulation of an extensible capsule using regularized Stokes kernels and overset finite differences
Dhwanit Agarwal, George Biros
In this paper, we present a novel numerical scheme for simulating deformable and extensible capsules suspended in a Stokesian fluid. The main feature of our scheme is a partition-o…
RCHOL: Randomized Cholesky Factorization for Solving SDD Linear Systems
Chao Chen, Tianyu Liang, George Biros
We introduce a randomized algorithm, namely RCHOL, to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian). From a graph perspecti…