Related papers: An Efficient Finite Difference-based Implicit Solv…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
A novel boundary element formulation for solving problems involving eddy currents in the thin skin depth approximation is developed. It is assumed that the time-harmonic magnetic field outside the scatterers can be described using the…
We present fast, spatially dispersionless and unconditionally stable high-order solvers for Partial Differential Equations (PDEs) with variable coefficients in general smooth domains. Our solvers, which are based on (i) A certain "Fourier…
We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces;…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
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…
We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen--Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method.…
Impurity solvers play an essential role in the numerical investigation of strongly correlated electrons systems within the "dynamical mean field" approximation. Recently, a new class of continuous-time solvers has been developed, based on a…
We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
Intelligent reflecting surface (IRS) that enables the control of the wireless propagation environment has been looked upon as a promising technology for boosting the spectrum and energy efficiency in future wireless communication systems.…
In this paper, we propose a horizontal type method of lines numerical scheme for the unsteady Euler-Bernoulli beam equation. The problem is initially reformulated as a first order system of initial value problems and a suitable one-step…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
In this paper, we observe a fixed number of unknown $2\pi$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common…