SC Faculty Bryan Quaife Discusses Simulation of a 2D Stokes Equation in Porous Media

Applied mathematician and Scientific Computing faculty Bryan Quaife attended a recent workshop on Fast Direct Solvers. The workshop was organized to exchange ideas on topics related to fast direct solvers, structured matrices, sparsity and data sparsity, structured preconditioning, high performance computing, fast PDE and IE solution, high order discretizations, related applications, and other relevant subjects.

Quaife’s presentation considered a boundary integral equation (BIE) formulation of the two-dimensional Stokes equation in a porous geometry. Quaife and collaborators Eric Darve and Pieter Coulier applied the inverse fast multipole method (IFMM) to precondition the linear system, then examined the effect of the preconditioner’s tolerance and compared its efficacy with a block-diagonal preconditioner on several geometries.

"The goal of a direct solver is to take advantage of low rank structure of linear systems to develop efficient solvers and preconditioners. The workshop brought together renowned experts, junior faculty, and Ph.D. students from a small research community. The exchange of ideas made it clear that direct solvers have become an important class of numerical methods for solving problems in interpolation, fluid dynamics, domain decomposition, and more," said Quaife.

The workshop was hosted November 12-13 in West Lafayette, Indiana at Purdue’s Center for Computational & Applied Mathematics. A widely dispersed set of scholars attended, with contributors and invited speakers from the U.S., Greece, Russia, Saudi Arabia and France.

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