arXiv subjects

Yann-Meing Law

Publications and source records attributed to Yann-Meing Law.

8 recordsLinked to original sources

arXiv2026

Waves 2026 Book of Abstracts

WAVES 2026, 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation Concordia University (John Molson Building), Montreal, Canada, June 22-26, 2026 WAVES 2026 is the seventeenth meeting in a long-running biennial series that has, throughout its history, alternated between Europe and North America to advance the mathematical and numerical study of wave propagation. Hosted at the John Molson Building of Concordia University in Montreal from June 22 to 26, 2026, the conference continues this tradition as a leading international forum where theory, computation, and application meet. The scientific program spans the full breadth of mathematical and numerical techniques for wave phenomena, from the modeling and analysis of the governing partial differential equations to the design, analysis, and implementation of efficient computational methods. Representative themes include acoustic, electromagnetic, elastic, and seismic wave propagation; scattering and inverse problems; high-frequency and asymptotic methods; finite element, boundary integral, and time-domain discretizations; and absorbing boundary conditions and domain truncation, with applications reaching across the physical sciences and engineering.

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arXiv2025

The high-order Hermite discrete correction function method for surface-driven electromagnetic problems

The Hermite-Taylor method evolves all the variables and their derivatives through order $m$ in time to achieve a $2m+1$ order rate of convergence. The data required at each node of the staggered Cartesian meshes used by this method makes the enforcement of boundary and interface conditions challenging. In this work, we propose a novel correction function method, referred to as the discrete correction function method, which provides all the data required by the Hermite method near the surface where a condition is enforced. The flexibility of the resulting Hermite-Taylor discrete correction function method is demonstrated by considering a wide range of problems, including those with variable coefficients, discontinuous solutions at the interface, and generalized sheet transition conditions. Although the focus of this work is on Maxwell's equations, this high-order method can be adapted to other linear wave systems. Several numerical examples in two space dimensions are performed to verify the properties of the proposed method, including long-time simulations.

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arXiv2025

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 embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$ in each Cartesian coordinate. This makes the development of a systematic approach to enforce boundary and interface conditions difficult. Here we use the correction function method to update the numerical solution where the Hermite-Taylor method cannot be applied directly. Time derivatives of boundary and interface conditions, converted into spatial derivatives, are enforced to obtain a stable method and relax the time-step size restriction of the Hermite-Taylor correction function method. The proposed high-order method offers a flexible systematic approach to handle embedded boundary and interface problems, including problems with discontinuous solutions at the interface. This method is also easily adaptable to other first order hyperbolic systems.

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arXiv2025

A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations

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 nonlinear algebraic solver, requiring solving instead small local linear systems for which the dimension is independent of the order. The implementation of order adaptive algorithms is straightforward in this setting, making the resulting p-adaptive Hermite method appealing for the simulations of soliton-like wave propagation.

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arXiv2023

The Hermite-Taylor Correction Function Method for Maxwell's Equations

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. Unfortunately its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor Correction Function method, which provides exactly such a systematic approach for handing boundary conditions. Here we focus on Maxwell's equations but note that the method is easily extended to other hyperbolic problems.

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arXiv2022

High-order FDTD schemes for Maxwell's interface problems with discontinuous coefficients and complex interfaces based on the Correction Function Method

We propose high-order FDTD schemes based on the Correction Function Method (CFM) for Maxwell's interface problems with discontinuous coefficients and complex interfaces. The key idea of the CFM is to model the correction function near an interface to retain the order of a finite difference approximation. For this, we solve a system of PDEs based on the original problem by minimizing an energy functional. The CFM is applied to the standard Yee scheme and a fourth-order FDTD scheme. The proposed CFM-FDTD schemes are verified in 2-D using the transverse magnetic mode (TM$_z$). Numerical examples include scattering of magnetic and non-magnetic dielectric cylinders, and problems with manufactured solutions using various complex interfaces and discontinuous piecewise varying coefficients. Long-time simulations are also performed to provide numerical evidences of the stability of the proposed numerical approach. The proposed CFM-FDTD schemes achieve up to fourth-order convergence in $L^2$-norm and provide approximations devoid of spurious oscillations.

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arXiv2021

FDTD schemes for Maxwell's equations with embedded perfect electric conductors based on the correction function method

In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell's equations with embedded perfect electric conductor (PEC) boundary conditions. The CFM uses a minimization procedure to compute a correction to a given FD scheme in the vicinity of the embedded boundary to retain its order. The minimization problem associated with CFM approaches is analyzed in the context of Maxwell's equations with embedded boundaries. In order to obtain a well-posed problem, we propose fictitious interface conditions to fulfill the lack of information, namely the surface current and charge density, on the embedded boundary. Fictitious interfaces can induce some issues for long time simulations and therefore the penalization coefficient associated with fictitious interface conditions must be chosen small enough. We introduce CFM-FDTD schemes based on the well-known Yee scheme and a fourth-order staggered FDTD scheme. Long time simulations and convergence studies are performed in 2-D for various geometries of the embedded boundary. CFM-FDTD schemes have shown high-order convergence.

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arXiv2020

Treatment of complex interfaces for Maxwell's equations with continuous coefficients using the correction function method

We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are modeled by a system of PDEs based on Maxwell's equations with interface conditions. To be able to compute approximations of correction functions, a functional that is a square measure of the error associated with the correction functions' system of PDEs is minimized in a divergence-free discrete functional space. Afterward, approximations of correction functions are used to correct a FDTD scheme in the vicinity of an interface where it is needed. We perform a perturbation analysis on the correction functions' system of PDEs. The discrete divergence constraint and the consistency of resulting schemes are studied. Numerical experiments are performed for problems with different geometries of the interface. A second-order convergence is obtained for a second-order FDTD scheme corrected using the CFM. High-order convergence is obtained with a corrected fourth-order FDTD scheme. The discontinuities within solutions are accurately captured without spurious oscillations.

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