Related papers: Analysis of a New Space-Time Parallel Multigrid Al…
The direct numerical simulation of metal additive manufacturing processes such as laser powder bed fusion is challenging due to the vast differences in spatial and temporal scales. Classical approaches based on locally refined finite…
In this paper, we develop sparse grid central discontinuous Galerkin (CDG) scheme for linear hyperbolic systems with variable coefficients in high dimensions. The scheme combines the CDG framework with the sparse grid approach, with the aim…
In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in porous media with thermal memory with random…
We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…
A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed…
The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…
This paper presents Space-Time MultiGrid (STMG) methods which are suitable for performing topology optimisation of transient heat conduction problems. The proposed methods use a pointwise smoother and uniform Cartesian space-time meshes.…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
The present work addresses the Cauchy problem for an abstract nonlinear system of coupled hyperbolic equations associated with the Timoshenko model in a real Hilbert space. Our purpose is to develop and delve into a temporal discretization…
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…
We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our most favourable scheme relies on a self-adjoint local dG (LDG) discretization of the…
In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete and fully discrete schemes are presented and analyzed.…
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…
We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
We propose the first optimal geometric multigrid solver for hybrid high-order discretizations that can handle arbitrary polytopal agglomeration hierarchies in both two and three dimensions. The key ingredient is the use of modified skeleton…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…