23 citations · 73 across the 31 of their papers we have counts for
33 papers
Waves 2026 Book of Abstracts
Lise-Marie Imbert-Gerard, Chrysoula Tsogka, Daniel Appelo +4
WAVES 2026, 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation Concordia University (John Molson Building), Montreal, Canada, June 22-26, 2026…
The WaveHoltz Heterogeneous Multiscale Method
Amit Rotem, Olof Runborg, Daniel Appelö
We consider the numerical solution of the wave equation in materials with rapidly varying coefficients, and time harmonic sources. For these problems, direct discretization is proh…
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…
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…
High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach
Spencer Lee, Daniel Appelo
This work introduces the High-Order Hermite Optimization (HOHO) method, an open-loop discrete adjoint method for quantum optimal control. Our method is the first of its kind to eff…
A -Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations
Yann-Meing Law, Zhichao Peng, Daniel Appelö +1
In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any…
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…
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…
Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations
Daniel Appelö, Yingda Cheng
In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to cap…
Energy-Conserving Hermite Methods for Maxwell's Equations
Daniel Appelo, Thomas Hagstrom, Yann-Meing Law-Kam-Cio
Energy-conserving Hermite methods for solving Maxwell's equations in dielectric and dispersive media are described and analyzed. In three space dimensions methods of order to…
Mathematical approaches for characterization, control, calibration and validation of a quantum computing device
Zhichao Peng, Daniel Appelo, N. Anders Petersson +2
Quantum computing has received significant amounts of interest from many different research communities over the last few years. Although there are many introductory texts that foc…
The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems
Yann-Meing Law, Daniel Appelö, Thomas Hagstrom
We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the ele…
Noise-specific beats in the higher-level Ramsey curves of a transmon qubit
L. A. Martinez, Z. Peng, D. Appelö +4
In the higher levels of superconducting transmon devices, and more generally charge sensitive devices, measurements made in the presence of low-frequency time-correlated $1…
The Hermite-Taylor Correction Function Method for Maxwell's Equations
Yann-Meing Law, Daniel Appelö
The Hermite-Taylor method, introduced in 2005 by Goodrich, Hagstrom and Lorenz, is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfo…
Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation
Fortino Garcia, Daniel Appelö, Olof Runborg
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy…
El-WaveHoltz: A Time-Domain Iterative Solver for Time-Harmonic Elastic Waves
Daniel Appelö, Fortino Garcia, Allen Alvarez Loya +1
We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acou…
Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
Zhichao Peng, Daniel Appelö, Shuang Liu
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell sti…
An Energy-Based Discontinuous Galerkin Method with Tame CFL Numbers for the Wave Equation
Daniel Appelö, Lu Zhang, Thomas Hagstrom +1
We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining spatial staggering with local…
Energy-based discontinuous Galerkin difference methods for second-order wave equations
Lu Zhang, Daniel Appelö, Thomas Hagstrom
We combine the newly-constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second order form. The approximation properties…
A Hermite Method with a Discontinuity Sensor for Hamilton-Jacobi Equations
Allen Alvarez Loya, Daniel Appelö
We present a Hermite interpolation based partial differential equation solver for Hamilton-Jacobi equations. Many Hamilton-Jacobi equations have a nonlinear dependency on the gradi…
Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
Daniel Appelo, Kiera van der Sande, Nathan Albin
Fourier continuation is an approach used to create periodic extensions of non-periodic functions in order to obtain highly-accurate Fourier expansions. These methods have been used…
EM-WaveHoltz: A flexible frequency-domain method built from time-domain solvers
Zhichao Peng, Daniel Appelö
A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite syste…
An energy-based summation-by-parts finite difference method for the wave equation in second order form
Siyang Wang, Daniel Appelö, Gunilla Kreiss
We develop a new finite difference method for the wave equation in second order form. The finite difference operators satisfy a summation-by-parts (SBP) property. With boundary con…
Accuracy of spectral element method for wave, parabolic and Schrödinger equations
Hao Li, Daniel Appelö, Xiangxiong Zhang
The spectral element method constructed by the () continuous finite element method with -point Gauss-Lobatto quadrature on rectangular meshes is a popular hig…