SIAM Journal on Scientific Computing

For scalar and vector-valued elliptic boundary value problems with discontinuous coefficients across geometrically complicated interfaces, a composite finite element approach is developed. Composite basis functions are constructed, mimicking the ...

We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In ...

A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a ...

We propose an a posteriori error estimation technique for the computation of average functionals of solutions for nonlinear time dependent problems based on duality techniques. The exact solution is assumed to have a periodic or quasi-periodic behavior ...

The finite-element spatial discretization of the linear shallow-water equations is examined in the context of several temporal discretization schemes. Three finite-element pairs are considered, namely, the $P^{}_{0}-P^{}_{1}$, $P^{NC}_{1}-P^{}_{1}$, and ...

We investigate the transition of a quantum wave-packet through a one-dimensional avoided crossing of molecular energy levels when the energy levels at the crossing point are tilted. Using superadiabatic representations, and an approximation of the ...

We introduce a new higher order scheme for computing a tangentially stabilized curve shortening flow with a driving force represented by an intrinsic partial differential equation for an evolving curve position vector. Our new scheme is a combination of ...

A simple nonrecursive form of the tensor decomposition in $d$ dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable ...

A general procedure for constructing conservative numerical integrators for time-dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretized version of the invariant are developed for ...

A treecode is presented for evaluating sums defined in terms of the multiquadric radial basis function (RBF), $\phi({\bf x}) = (|{\bf x}|^2+c^2)^{1/2}$, where ${\bf x} \in \mathbb{R}^3$ and $c \ge 0$. Given a set of $N$ nodes, evaluating an RBF sum ...

A well-balanced scheme for an isolated gravitational hydrodynamic system is defined as a scheme which exactly preserves an isothermal hydrostatic solution. In this paper, a well-balanced gas-kinetic symplecticity-preserving BGK (SP-BGK) scheme is ...

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms ...

In this paper, we develop a third order accurate fast marching method for the solution of the eikonal equation in two dimensions. There have been two obstacles to extending the fast marching method to higher orders of accuracy. The first obstacle is ...

In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary ...

Surface integral-equation methods accelerated with the multilevel fast multipole algorithm (MLFMA) provide a suitable mechanism for electromagnetic analysis of real-life dielectric problems. Unlike the perfect-electric-conductor case, discretizations of ...

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton-Jacobi equations to which it belongs, have a wide range of applications from ...

We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order ...

Chebfun is an established software system for computing with functions of a real variable, but its capabilities for handling functions with singularities are limited. Here an analogous system is described based on sinc function expansions instead of ...

An icosahedral-hexagonal grid on the two-sphere is created by dividing the faces of an icosahedron and projecting the vertices onto the sphere. This grid and its Voronoi tessellation have several desirable features for numerical simulations of physical ...

We examine the dispersion and dissipation properties of the Gauss and Gauss-Lobatto discontinuous Galerkin spectral element methods (DGSEMs), for linear wave propagation problems. We show that the inherent underintegration in the Gauss-Lobatto variant ...

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy—even on parallel processors—unlike the classical (deterministic) alternatives. We adapt one of these randomized ...

Newton-Krylov methods, a combination of Newton-like methods and Krylov subspace methods for solving the Newton equations, often need adequate preconditioning in order to be successful. Approximations of the Jacobian matrices are required to form ...

We present a numerically fast reduced filtering strategy, the Fourier domain Kalman filter with appropriate interpolations to account for irregularly spaced observations of complex turbulent signals. The design of such a reduced filter involves: (i) ...

We explore a stochastic optimal control problem for incompressible flow in a channel by using reduced-order modeling (ROM) based on proper orthogonal decomposition (POD). The control acts on a portion of the boundary and has a stochastic perturbation. ...

This paper is concerned with the superconvergence of the discontinuous Galerkin solutions for delay differential equations with proportional delays vanishing at $t = 0$. Two types of superconvergence are analyzed here. The first is based on ...

The biennial Copper Mountain Conference on Iterative Methods was held April 4–9, 2010. This meeting included more than 140 presentations covering many scientific computing areas, such as uncertainty quantification, optimization, Markov chains, saddle-...

We provide formulas for the norm of the error when solving nonsymmetric linear systems with the full orthogonalization method (FOM) and the generalized minimum residual method (GMRES) as well as relations between the error norm and the residual norm. ...

We consider sparse linear systems, where a set of “interior” degrees of freedom have been eliminated in order to reduce the problem size. This elimination is assumed to be local, so the “interior” principal submatrix is block-diagonal, and the resulting ...

Almost all approaches to solving partial differential equations (PDEs) are based upon a spatial discretization of the computational domain—a grid. This paper presents an algorithm to generate, store, and traverse a hierarchy of $d$-dimensional Cartesian ...

We analyze a class of modified augmented Lagrangian-based preconditioners for both stable and stabilized finite element discretizations of the steady incompressible Navier-Stokes equations. We study the eigenvalues of the preconditioned matrices ...