12 papers · 1 filter
LR-WaveHoltz: A Low-Rank Helmholtz Solver
Andreas Granath, Daniel Appelö, Siyang Wang
We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter…
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…
Convergence of the Semi-Discrete WaveHoltz Iteration
Amit Rotem, Olof Runborg, Daniel Appelo
In this paper we prove that for stable semi-discretizations of the wave equation for the WaveHoltz iteration is guaranteed to converge to an approximate solution of the correspondi…
A new cross approximation for Tucker tensors and its application in Tucker-Anderson Acceleration
Daniel Appelö, Yingda Cheng
This paper proposes two new algorithms related to the Tucker tensor format. The first method is a new cross approximation for Tucker tensors, which we call Cross-DEIM. Cross$^2…
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…