University of Texas at Austin

Past Event: CSEM Student Forum

SlabLU: A Novel Sparse Direct Solver

Anna Yesypenko, CSEM PhD Student, Oden Institute, UT Austin

12:30 – 1PM
Friday Nov 18, 2022

POB 6.304

Abstract

This talk presents slabLU, a novel sparse direct solver framework for elliptic PDEs on rectangular domains. SlabLU decomposes the domain into a sequence of thin slabs. In this construction, the degrees of freedom internal to each slab are eliminated in parallel, yielding a reduced system defined on the slab interfaces. This resulting system can be efficiently factorized directly.

The general two-level framework is simple to implement, easy to parallelize, and can be accelerated via batched linear algebra and GPU computations. Slab-based decomposition schemes are a compelling alternative to multi-level nested dissection schemes, which have superior asymptotic flop complexity but are communication-intensive and challenging to parallelize.

The methodology applies generally to many PDE discretizations. SlabLU interfaces well with high order multi-domain spectral collocation schemes, making the solver a particularly powerful tool for solving problems with highly oscillatory solutions, such as variable coefficient Helmholtz. Numerical results for 2D problems will be shown.

Biography

Anna's work is concerned with developing efficient algorithms for scientific computing, namely for the solution of differential and integral equations. The overarching theme of her work is that dense solution operators representing Green's functions often have structure that allow them to be applied quickly. She is concerned with designing solvers that parallelize well and attain high performance on modern latency-bound architectures.

B.S., Computer Science, Cornell University (2017)
M.S., Computational Science, Engineering, and Mathematics, The University of Texas at Austin (2019)

Anna is co-advised by Gunnar Martinsson and George Biros.

SlabLU: A Novel Sparse Direct Solver

Event information

Date
12:30 – 1PM
Friday Nov 18, 2022
Location POB 6.304
Hosted by Shane McQuarrie