SIAM Journal on Scientific Computing

A hybrid scheme, based on the high order nonlinear characteristicwise weighted essentially nonoscillatory (WENO) conservative finite difference scheme and the spectral-like linear compact finite difference scheme, has been developed for capturing shocks ...

We derive a representation formula for harmonic polynomials and Laurent polynomials in terms of densities of the double-layer potential on bounded piecewise smooth and simply connected domains. From this result, we obtain a method for the numerical ...

A common task in computational physics is the convolution of a translation invariant, free-space Green's function with a smooth and compactly supported source density. Fourier methods are natural in this context but encounter two difficulties. First, the ...

This work is a further development and the culmination along our research line of interface tracking in two dimensions [Zhang and Liu, J. Comput. Phys., 27 (2008), pp. 4063--4088; Zhang, SIAM J. Numer. Anal., 51 (2013), pp. 2822--2850; Zhang and Fogelson, ...

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian gradient flow ...

In shape optimization it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy--Riemann equations. Our method allows us to deform meshes in a ...

We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well as on ...

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that, using this condition, the iterative refinement algorithm terminates successfully. Additionally we provide an $O(n)$ ...

This paper investigates the approximation of the shallow water equations with topography and friction, using continuous finite elements. A new, second-order, parameter-free, well-balanced and positivity preserving explicit approximation technique is ...

Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation are presented. Both methods use $(m+1)^d$ degrees of freedom per node for the displacement in $d$ dimensions; the dissipative and conservative methods achieve ...

The bootstrap algebraic multigrid framework allows for the adaptive construction of algebraic multigrid methods in situations where geometric multigrid methods are not known or not available at all. While there has been some work on adaptive coarsening in ...

Sensitivity analysis (SA) is the study of how the output of a mathematical model is affected by changes in the inputs. SA is widely studied, due to its many applications: uncertainty quantification, quick evaluation of close solutions, and optimization, to ...

We consider in this paper gradient flows with disparate terms in the free energy that cannot be efficiently handled with the scalar auxiliary variable (SAV) approach, and we develop the multiple scalar auxiliary variable (MSAV) approach to deal with these ...

We consider a boundary value problem in weak form of a steady-state Riesz space-fractional diffusion equation (FDE) of order $2-\alpha$ with $0<\alpha<1$. By using a finite volume approximation technique on uniform grids, we obtain a large linear system, ...

We propose a new formulation of a low-order elliptic preconditioner for high-order triangular elements. In the preconditioner, the nodes of the low-order finite element problem do not necessarily coincide with the high-order nodes. Instead, the two spaces ...

We derive an algorithm for computing the wave-kernel functions $\cosh\sqrt{A}$ and $\mathrm{sinhc}\sqrt{A}$ for an arbitrary square matrix $A$, where $\mathrm{sinhc}z=\sinh(z)/z$. The algorithm is based on Padé approximation and the use of double angle ...

A second-order Crank--Nicolson finite difference method, integrating a fast approximation of an exact discrete absorbing boundary condition, is proposed for solving the one-dimensional Schrödinger equation in the whole space. The fast approximation is ...

Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a symmetric ...

The well-known interior point method for semidefinite progams can only be used to tackle problems of relatively small scales. First-order methods such as the the alternating direction method of multipliers (ADMM) have much lower computational cost per ...

In this paper we study the level set formulations of certain geometric evolution equations from a numerical point of view. Specifically, we consider the flow by powers greater than one of the mean curvature (PMCF) and the inverse mean curvature flow (...

An adaptive finite element method for eigenvalue problems is proposed based on the multilevel correction scheme. Different from the standard adaptive finite element method which requires solving eigenvalue problems on adaptively refined triangulations, ...

A lattice Boltzmann model for the propagation and sharpening of phase boundaries that arise in applications such as multiphase flow is presented. The sharpening is accomplished through an artificial compression term that acts in the vicinity of the ...

We developed a novel collisional $N$-body numerical integrator, which we termed the Simò integrator, designed to model the electrostatic $N$-body problem of charged particle beams. It is proposed to accurately resolve close encounters and overcome ...

The fluid-structure interaction (FSI) problem has received great attention in the last few years, mainly because it is present in many physical systems, industrial applications, and almost every biological system. In the parallel computational field, ...

Asynchronous iterations have been investigated more and more for both scaling and fault-resilience purposes on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper ...

We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss--Legendre quadrature rules. Our focus is on making the evaluation practical for a wide range of ...

We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator ...

We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accuracy with respect to an error norm, and the computation rate, a cost-benefit ...

This work presents algorithms for the efficient implementation of discontinuous Galerkin methods with explicit time stepping for acoustic wave propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial step towards efficiency is to ...

We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on the ...