Physical Sciences and Mathematics Commons^™

Spacetime Numerical Techniques For The Wave And Schrödinger Equations, Paulina Ester Sepùlveda Salas

Dissertations and Theses

The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain. Therefore, spacetime problems can be studied as boundary value problems, where initial conditions are considered as part of the spacetime boundary conditions.

When seeking solutions to these problems, it is natural to ask what are the correct spaces of functions to choose, to obtain wellposedness. This motivates the study …

A Parallel Mesh Generator In 3d/4d, Kirill Voronin

Portland Institute for Computational Science Publications

In the report a parallel mesh generator in 3d/4d is presented. The mesh generator was developed as a part of the research project on space-time discretizations for partial differential equations in the least-squares setting. The generator is capable of constructing meshes for space-time cylinders built on an arbitrary 3d space mesh in parallel. The parallel implementation was created in the form of an extension of the finite element software MFEM. The code is publicly available in the Github repository

High-Order Method For Evaluating Derivatives Of Harmonic Functions In Planar Domains, Jeffrey S. Ovall, Samuel E. Reynolds

Mathematics and Statistics Faculty Publications and Presentations

We propose a high-order integral equation based method for evaluating interior and boundary derivatives of harmonic functions in planar domains that are specified by their Dirichlet data.