相关论文: A limited-memory block bi-diagonal Toeplitz precon…
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…
This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or…
In this paper, we study a parallel-in-time (PinT) algorithm for all-at-once system from a non-local evolutionary equation with weakly singular kernel where the temporal term involves a non-local convolution with a weakly singular kernel and…
Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated…
Starting from the spectral analysis of g-circulant matrices, we consider a new multigrid method for circulant and Toeplitz matrices with given generating function. We assume that the size n of the coefficient matrix is divisible by g \geq 2…
A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Toeplitz Block Toeplitz matrices using minimized matrix-vector products, with a complexity…
First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is…
We present novel improvements in the context of symbol-based multigrid procedures for solving large block structured linear systems. We study the application of an aggregation-based grid transfer operator that transforms the symbol of a…
In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structure-preserving finite-element approximation with…
The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications in finance, chaotic dynamics, optical physics, and…
In this work we present a space-time least squares isogeometric discretization of the Schr\"odinger equation and propose a preconditioner for the arising linear system in the parametric domain. Exploiting the tensor product structure of the…
We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…
In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, including the heat equation and the non-steady…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution…