Timothy Warburton

Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods

We construct and analyze new local radiation boundary condition sequences for first-order, isotropic, hyperbolic systems. The new conditions are based on representations of solutions of the scalar wave equation in terms of modes which both propagate and decay. Employing radiation boundary conditions which are exact on discretizations of the complete wave expansions essentially eliminates the long time nonuniformities encountered when using the standard local methods (perfectly matched layers or Higdon sequences). Specifically, we prove that the cost in terms of degrees-of-freedom per boundary point scales with

Radiation boundary conditions for time-dependent waves based on complete plane wave expansions

lnfrac{1}{epsilon}cdotlnfrac{cT}{delta}

Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes

, where

GPU-accelerated discontinuous Galerkin methods on hybrid meshes

epsilon

High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

is the error tolerance,

GPU-accelerated Bernstein-Bezier discontinuous Galerkin methods for wave problems

T

Weight-Adjusted Discontinuous Galerkin Methods: Wave Propagation in Heterogeneous Media

is the simulation time, and

Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes

delta

Solving Wave Equations on Unstructured Geometries

is the separation between the source-containing region and the artificial boundary. Choosing

Orthogonal Bases for Vertex-Mapped Pyramids

deltasimlambda