High-order accurate methods for time-domain electromagnetics
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A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh re ...
A simple approach is extended for the simulation of Kerr-nonlinear and/or dispersive media through the finite-difference time-domain method. The scheme is able to include different types of linear and nonlinear dispersion in a single and unified formulatio ...
Institute of Electrical and Electronics Engineers2010
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emerging importance to the widely used FDTD. The benefits of DG methods include geometric flexibility, high-order accuracy, explicit timeadvancement, and very high pa ...
We describe a multiscale finite element (FE) solver for elliptic or parabolic problems with highly oscillating coefficients. Based on recent developments of the so-called heterogeneous multiscale method (HMM), the algorithm relies on coupled macro- and mic ...
This paper investigates the particular problem of matrices appearing during the modeling of Integrated Circuits with Finite Integration Technique (FIT) method. We present the key points of FIT approach followed by an illustration of the structure and the p ...
In this paper we address the numerical approximation of the incompressible Navier-Stokes equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the inco ...
With increasing power densities, runtime thermal management is becoming a necessity in today’s systems, especially so for highly integrated Multi-Processor Systems-on-Chip (MPSoCs). In this paper, we propose a neural network (NN) based approach to implemen ...
Standard high order Galerkin methods, such as pure spectral or high order finite element methods, have insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization strategies for pure spectral m ...
A high-order implicit-explicit additive Rung-Kutta time integrator is implemented in a particle-in-cell method based on a high-order discontinuous Galerkin Maxwell solver for the simulation of plasmas. The method enforces Gauss law by a hyperbolic divergen ...