We conduct simulations for the 3D unsteady state anisotropic diffusion process with DT-MRI data in the human brain by discretizing the governing diffusion equation on Cartesian grid and adopting a high performance differential–algebraic equation (DAE) solver, the parallel version of implicit differential–algebraic (IDA) solver, to tackle the resulting large scale system of DAEs. Parallel precon...

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton–Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower–...

We developed a fast iterative solver for computing time-harmonic acoustic waves scattered by an elastic object in layered media. The discretization of the problem was performed using a finite element method with linear elements based on a locally body-fitted uniform triangulation. We used a domain decomposition preconditioner in the iterative solution of the resulting system of linear equations...

Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and eva...

In this paper we describe an embedded iterative scheme based on the GMRES method and implemented in combination with the Fast Multipole Method for the solution of large electromagnetic scattering problems expressed in an integral formulation. In our scheme, we use a Frobenius-norm minimization preconditioner to speed-up the inner iterations, and the M-V products within the inner and the outer s...

Abstract. This contribution compares the efficiency of Rosenbrock time integration schemes with ESDIRK schemes, applicable to unsteady flow and fluid-structure interaction simulations. Compared to non-linear ESDIRK schemes, the linear implicit RosenbrockWanner schemes require subsequent solution of the same linear systems with different right hand sides. By solving the linear systems with the i...

We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfectly matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the subdomains where the emphasis is on the boundary values of the intermediate waves. This approach can be viewed as an effective approximation of an additive deco...

Abstract. We consider a norm-preconditioning approach for the solution of discontinuous Galerkin finite element discretizations of second order PDE with non-negative characteristic form. In particular, we perform an analysis for the general case of discontinuous hp-finite element discretizations. Our solution method is a norm-preconditioned threeterm GMRES routine. We find that for symmetric po...

Block Toeplitz matrices are a special class of that exhibit reduced memory requirements and complexity matrix-vector multiplications. We herein present an efficient computational approach to solve sequence block systems arising from system with multiple right-hand sides. Two different numerical schemes implemented for the solution based on global variants generalized minimal residual (GMRES) me...

We investigate an iterative method for the solution of time-periodic parabolic PDE constrained optimization problems. It is an inexact Sequential Quadratic Programming (iSQP) method based on the Newton-Picard approach. We present and analyze a linear quadratic model problem and prove optimal mesh-independent convergence rates. Additionally, we propose a two-grid variant of the Newton-Picard met...