Related papers: Spectral analysis and multigrid preconditioners fo…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…
We present the Method Of Lines (MOL), which is based on the spectral collocation method, to solve space-fractional advection-diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the…
Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…
A framework for Chebyshev spectral collocation methods for the numerical solution of functional and delay differential equations (FDEs and DDEs) is described. The framework combines interpolation via the barycentric resampling matrix with a…
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…
Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochastic) inputs. We consider the related problem of a matrix…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
A parallel and nested version of a frequency filtering preconditioner is proposed for linear systems corresponding to diffusion equation on a structured grid. The proposed preconditioner is found to be robust with respect to jumps in the…
The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the…
The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov--Galerkin method…
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz…
This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions, combining high-resolution compact schemes with low-order…
The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radiation diffusion and frequency-dependent diffusion equations…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems. We propose two novel strategies for…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in…