6 papers
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…
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…
Preconditioning Low Rank Generalized Minimal Residual Method (GMRES) for Implicit Discretizations of Matrix Differential Equations
Shixu Meng, Daniel Appelo, Yingda Cheng
This work proposes a new class of preconditioners for the low rank Generalized Minimal Residual Method (GMRES) for multiterm matrix equations arising from implicit timestepping of…
Kraus is King: High-order Completely Positive and Trace Preserving (CPTP) Low Rank Method for the Lindblad Master Equation
Daniel Appelo, Yingda Cheng
We design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Our methods preserves…