5 papers
Numerical Study of Eigenvector Deflation to Accelerate the WaveHoltz Method
Daniel Appelo, William D. Henshaw, Zhichao Peng
We present a numerical study of eigenvector deflation as a means of accelerating the WaveHoltz method for solving the Helmholtz equation. For energy-conserving (Dirichlet or Neuman…
A Multi-Frequency Helmholtz Solver Based on the WaveHoltz Algorithm
Daniel Appelö, Francis Appiah, Jeffrey W. Banks +3
We develop and analyze a new approach for simultaneously computing multiple solutions to the Helmholtz equation for different frequencies and different forcing functions. The new M…
EigenWave: An Optimal O(N) Method for Computing Eigenvalues and Eigenvectors by Time-Filtering the Wave Equation
Daniel Appelo, Jeffrey W. Banks, William D. Henshaw +2
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz sche…
An Optimal O(N) Helmholtz Solver for Complex Geometry using WaveHoltz and Overset Grids
Daniel Appelo, Jeffrey W. Banks, William D. Henshaw +1
We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of th…
High Order Accurate Hermite Schemes on Curvilinear Grids with Compatibility Boundary Conditions
Allen Alvarez Loya, Daniel Appelö, William D. Henshaw
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more stan…