SIAM Journal on Scientific Computing

Reasonable point set selection is of paramount importance to the accuracy of high-dimensional integrals that will be encountered in various disciplines. In the present paper, to improve the point selection and to overcome the computational complexity of ...

We show that symplectic Runge--Kutta methods provide effective symplectic integrators for Hamiltonian systems with index 1 constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints ...

In this paper we develop a new limiter for linear reconstruction on non-coordinate-aligned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two dimensional and linearity preserving. It separately limits ...

In this work we extend the qualitative reconstruction method for inverse source problems for time-harmonic acoustic and electromagnetic waves in free space, recently developed in [R. Griesmaier, M. Hanke, and T. Raasch, SIAM J. Sci. Comput., 34 (2012), pp. ...

We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare it to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an uncorrelated Markov ...

We consider the problem of solving linear systems of equations that arise in the numerical solution of singularly perturbed ordinary and partial differential equations of reaction-diffusion type. Standard discretization techniques are not suitable for such ...

We describe a high-order accurate methodology for the numerical simulation of time-harmonic waves governed by the Helmholtz equation. Our approach combines compact finite difference schemes that provide an inexpensive venue toward high-order accuracy with ...

We present a robust method for choosing multivariate polynomial interpolation nodes. Our algorithm is an optimization method to greedily minimize a measure of interpolant sensitivity, a variant of a weighted Lebesgue function. Nodes are therefore chosen that ...

We propose a suitable model reduction paradigm---the certified reduced basis method (RB)---for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for ...

This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via ...

In this work, we discuss the approximation of elliptic problems with log-normal random coefficients using the Wick product and the Mikulevicius--Rozovskii formula. The main idea is that the multiplication between the log-normal coefficient and the gradient ...

The parareal algorithm, which permits us to solve evolution problems in a time parallel fashion, has created a lot of attention over the past decade. The algorithm has its roots in the multiple shooting method for boundary value problems, which in the ...

We propose a simple finite difference scheme for Navier--Stokes equations in primitive formulation on curvilinear domains. With proper boundary treatment and interplay between covariant and contravariant components, the spatial discretization admits exact ...

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix systems, is a field of numerical analysis that has recently been attracting much attention. In this paper, we ...

In this paper, we investigate an interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that directly applying the subspace conditions from the standard state space settings to ...

Topology is a natural mathematical tool for quantifying complex structures. In many applications, such as, for example, in the context of phase-field models in materials science, the structures of interest arise as sub- or superlevel sets of continuous ...

We present a novel method for pricing European options based on the wavelet approximation method and the characteristic function. We focus on the discounted expected payoff pricing formula and compute it by means of wavelets. We approximate the density ...

We investigate optimization problems in which the state is given in terms of fluid-structure interactions. The coupled problem is formulated with the help of the ALE (arbitrary Lagrangian--Eulerian) mapping. The solution approach is based on derivative-...

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-...

We present a general variable viscosity and variable density immersed boundary method that is first-order accurate in the variable density case and, for problems possessing sufficient regularity, second-order accurate in the constant density case. The ...

We derive an implicit-explicit (IMEX) formalism for the three-dimensional (3D) Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud resolving and mesoscale (flow in a 3D Cartesian domain) as well as ...

A homology and cohomology solver for finite element meshes is represented. It is an integrated part of the finite element mesh generator Gmsh. We demonstrate the exploitation of the cohomology computation results in a finite element solver and use an ...

We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations (ODEs) and is based ...

Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be ...

The Twelfth Copper Mountain Conference on Iterative Methods was held March 25--30, 2012, in Copper Mountain, Colorado. The meeting featured more than 150 presentations on a wide range of topics in scientific computing, including Krylov subspace methods, ...

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem by introducing the flow's vorticity as an ...

We present physics-based preconditioning and a time-stepping strategy for a moment-based scale-bridging algorithm applied to the thermal radiative transfer equation. Our goal is to obtain (asymptotically) second-order time accurate and consistent solutions ...

Krylov subspace methods are iterative methods for solving large, sparse linear systems and eigenvalue problems in a variety of scientific domains. On modern computer architectures, communication, or movement of data, takes much longer than the equivalent ...

In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a ...

Obtaining high resolution images of space objects from ground based telescopes is challenging, and often requires computational postprocessing methods to remove blur caused by atmospheric turbulence. In order for an image deblurring (deconvolution) algorithm ...