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We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…
A combined source integral equation (CSIE) is constructed on the basis of the electric field integral equation (EFIE) to solve electromagnetic radiation and scattering problems containing perfect electrically conducting bodies. It is…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
The requirement for continual improvement of idle speed control (ISC) performance is increasing due to the stringent regulation on emission and fuel economy these days. In this regard, a low-complexity offset-free explicit model predictive…
This paper presents an extension of the recently introduced planewave density interpolation (PWDI) method to the electric field integral equation (EFIE) formulation of problems of scattering and radiation by perfect electric conducting…
The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds over the past decade. During this time, advances have been made in (i) the development of accelerators that can be retrofitted with these solvers…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons is considered, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair…
We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical…
A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress…
We are aiming to identify the thin insulating inhomogeneities and small conductive inhomogeneities inside an electrically conducting medium by using multi-frequency electrical impedance tomography (mfEIT). The thin insulating…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for…
Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…