SIAM Journal on Scientific Computing

In the last decade, expression templates (ETs) have gained a reputation as an efficient performance optimization tool for C++ codes. This reputation builds on several ET-based linear algebra frameworks focused on combining both elegant and high-...

With the raw computing power of graphics processing units (GPUs) being more widely available in commodity multicore systems, there is an imminent need to harness their power for important numerical libraries such as LAPACK. In this paper, we consider ...

The nonlocal continuum dielectric model is an important extension of the classical Poisson dielectric model, but it is very expensive to be solved in general. In this paper, we prove that the solution of one commonly used nonlocal continuum dielectric ...

The optimal sensor-location problem is considered in the framework of variational data assimilation for a large-scale dynamical model governed by partial differential equations. This problem is formulated as an optimization problem for the design ...

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the ...

We present a fourth-order accurate algorithm for solving Poisson's equation, the heat equation, and the advection-diffusion equation on a hierarchy of block-structured, adaptively refined grids. For spatial discretization, finite-volume stencils are ...

Fast Marching and Fast Sweeping are the two most commonly used methods for solving the eikonal equation. Each of these methods performs best on a different set of problems. Fast Sweeping, for example, will outperform Fast Marching on problems where the ...

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, ...

The modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges. The extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine ...

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091-3120] to convection diffusion equations, we propose a nonconventional high order finite volume ...

We consider the numerical solution of a steady-state diffusion problem where the diffusion coefficient is the exponent of a random field. The standard stochastic Galerkin formulation of this problem is computationally demanding because of the nonlinear ...

Recent achievements in the field of tensor product approximation provide promising new formats for the representation of tensors in form of tree tensor networks. In contrast to the canonical $r$-term representation (CANDECOMP, PARAFAC), these new ...

In a wide number of applications in computational science and engineering the solution of large linear systems of equations with several right-hand sides given at once is required. Direct methods based on Gaussian elimination are known to be especially ...

We provide a new way to compute and evaluate Gaussian radial basis function interpolants in a stable way with a special focus on small values of the shape parameter, i.e., for “flat” kernels. This work is motivated by the fundamental ideas proposed ...

A new semidiscrete finite volume scheme for systems of hyperbolic conservation laws using the constrained transport method to evolve divergence-free vector fields on orthogonal curvilinear grids is presented. Our results are an extension of a ...

We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto-Sivashinsky equations. Time discretizations are constructed using linearly implicit schemes and spectral methods ...

Stochastic collocation (SC) methods for uncertainty quantification (UQ) in computational problems are usually limited to hypercube probability spaces due to the structured grid of their quadrature rules. Nonhypercube probability spaces with an irregular ...

This paper deals with variable-stepsize Nordsieck formulas applied to ordinary differential equations. It focuses on local and global error evaluation techniques in the mentioned numerical schemes. The error estimators are derived for both consistent ...

We present a simplified $h$-box method for integrating time-dependent conservation laws on embedded boundary grids using an explicit finite volume scheme. By using a method of lines approach with a strong stability preserving Runge-Kutta method in time, ...

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can ...

Using Wiener chaos expansion (WCE), we develop numerical algorithms for solving second-order linear parabolic stochastic partial differential equations (SPDEs). We propose a deterministic WCE-based algorithm for computing moments of the SPDE solutions ...

We present a new approach to treating nonlinear operators in reduced basis approximations of parametrized evolution equations. Our approach is based on empirical interpolation of nonlinear differential operators and their Fréchet derivatives. Efficient ...

The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard ...

Spectral approximations to nonlinear hyperbolic conservation laws require dissipative regularization for stability. The dissipative mechanism must, on the other hand, be small enough in order to retain the spectral accuracy in regions where the solution ...

A new method of spatial discretization for immersed boundary computations is introduced. Fluid velocity and pressure are obtained as weak solutions of the discretized fluid equations with respect to a wavelet basis of functions. The scaling function of ...

We present an alternative strategy for truncating the higher-order singular value decomposition (T-HOSVD). An error expression for an approximate Tucker decomposition with orthogonal factor matrices is presented, leading us to propose a novel truncation ...

It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a nonstationary diffusion equation. Implications of this result for adaptive kernel density estimation of the condensed density ...

We consider the iterative solution of large sparse symmetric positive definite linear systems. We present an algebraic multigrid method which has a guaranteed convergence rate for the class of nonsingular symmetric M-matrices with nonnegative row sum. ...

By using a spectral approach, we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. The quadrature is obtained from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite ...

A treecode algorithm is presented for the fast evaluation of multiquadric radial basis function (RBF) approximations. The method is a dual approach to one presented by Krasny and Wang, which applies far-field expansions to clusters of RBF centers (...