Related papers: A comparative study on low-memory iterative solver…
This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method. Modern implementations of high-order…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
In this paper, a new and efficient numerical algorithm by using weak Galerkin (WG) finite element methods is proposed for a type of fourth order problem arising from fluorescence tomography(FT). Fluorescence tomography is an emerging, in…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
We propose an implementation of a method based on Fourier analysis to obtain the Floquet characteristic exponents for periodic homogeneous linear systems, which shows a high precision. This implementation uses a variational principle to…
A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: (i) the memory usage is…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…
The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
In this paper, based on the limited memory techniques and subspace minimization conjugate gradient (SMCG) methods, a regularized limited memory subspace minimization conjugate gradient method is proposed, which contains two types of…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green…
In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…