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06/05/2023
Fast and high-order approximation of parabolic equations using hierarchical direct solvers and implicit Runge-Kutta methods
A stable and high-order accurate solver for linear and nonlinear parabol...
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01/25/2023
Mathematical approaches for characterization, control, calibration and validation of a quantum computing device
Quantum computing has received significant amounts of interest from many...
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01/04/2023
The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems
We propose a novel Hermite-Taylor correction function method to handle e...
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10/13/2022
The Hermite-Taylor Correction Function Method for Maxwell's Equations
The Hermite-Taylor method, introduced in 2005 by Goodrich, Hagstrom and ...
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05/24/2022
Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation
In this paper we extend analysis of the WaveHoltz iteration – a time-dom...
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05/24/2022
El-WaveHoltz: A Time-Domain Iterative Solver for Time-Harmonic Elastic Waves
We consider the application of the WaveHoltz iteration to time-harmonic ...
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04/12/2022
Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
We develop a universally applicable embedded boundary finite difference ...
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10/14/2021
An Energy-Based Discontinuous Galerkin Method with Tame CFL Numbers for the Wave Equation
We extend and analyze the energy-based discontinuous Galerkin method for...
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05/11/2021
A Hermite Method with a Discontinuity Sensor for Hamilton-Jacobi Equations
We present a Hermite interpolation based partial differential equation s...
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05/04/2021
Energy-based discontinuous Galerkin difference methods for second-order wave equations
We combine the newly-constructed Galerkin difference basis with the ener...
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04/30/2021
Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
Fourier continuation is an approach used to create periodic extensions o...
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03/27/2021
EM-WaveHoltz: A flexible frequency-domain method built from time-domain solvers
A novel approach to computing time-harmonic solutions of Maxwell's equat...
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03/02/2021
An energy-based summation-by-parts finite difference method for the wave equation in second order form
We develop an energy-based finite difference method for the wave equatio...
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02/28/2021
Accuracy of spectral element method for wave, parabolic and Schrödinger equations
The spectral element method constructed by the Q^k (k≥ 2) continuous fin...
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02/10/2020
Anderson Acceleration Using the H^-s Norm
Anderson acceleration (AA) is a technique for accelerating the convergen...
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01/27/2020
An energy-based discontinuous Galerkin method for semilinear wave equations
We generalize the energy-based discontinuous Galerkin method proposed in...
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01/14/2020
Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation
We present high order accurate numerical methods for the wave equation t...
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10/22/2019