Schwarz methods use a decomposition of the computational domain into subdomains and
need to impose boundary conditions on the subdomain boundaries. In domain truncation …

This paper presents a fast algorithm for computing transport properties of two-dimensional
Dirac operators with linear domain walls, which model the macroscopic behavior of the …

The paper describes a sparse direct solver for the linear systems that arise from the
discretization of an elliptic PDE on a two-dimensional domain. The scheme decomposes the …

Continuous enhancements and diversity in modern multi-core hardware, such as wider and
deeper core pipelines and memory subsystems, bring to practice a set of hard-to-solve …

We describe a fast, direct solver for elliptic partial differential equations on a two-
dimensional hierarchy of adaptively refined, Cartesian meshes. Our solver, inspired by the …

We prove sharp bounds on certain impedance-to-impedance maps (and their compositions)
for the Helmholtz equation with large wavenumber (ie, at high frequency) using …

We prove sharp bounds on certain impedance-to-impedance maps (and their compositions)
for the Helmholtz equation with large wavenumber (ie, at high-frequency) using …

This manuscript presents an efficient solver for the linear system that arises from the
hierarchical Poincaré–Steklov (HPS) discretization of three dimensional variable coefficient …

Elliptic partial differential equations (PDEs) arise in many areas of computational sciences
such as computational fluid dynamics, biophysics, engineering, geophysics and more. They …

The dissertation concerns numerical methods for approximately solving certain linear partial
differential equations. The foundation is a solution methodology for linear elliptic boundary …