相关论文: A PCG Implementation of an Elliptic Kernel in an O…

We present a GPU implementation of Algorithm NCL, an augmented Lagrangian method for solving large-scale and degenerate nonlinear programs. Although interior-point methods and sequential quadratic programming are widely used for solving…

Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…

We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain…

We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the non-uniqueness of the…

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new…

We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

Spurious numerical mixing is a frequent phenomenon in ocean models. In this paper, we present an efficient and robust methodology that defines the vertical grid motion so that this mixing is reduced. This motion is defined as the solution…

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness…

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…

We present a compact discontinuous Galerkin (CDG) method for an elliptic model problem. The problem is first cast as a system of first order equations by introducing the gradient of the primal unknown, or flux, as an additional variable. A…

In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…

We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element…

Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous properties. They can be used for arbitrary domains and support a…

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…

Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit…