SIAM Journal on Scientific Computing

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite ...

In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data are available. We propose a simple and efficient direct sampling method to locate inhomogeneities inside a homogeneous ...

Many engineering systems are subject to spatially distributed uncertainty, i.e., uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will, in general, change the statistical distribution of the system ...

We propose a Nitsche-based fictitious domain method for the three field Stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh. The dependent variables of velocity, pressure, and extra-stress ...

The numerical computation of barycentric Hermite interpolation may suffer from devastating inaccuracies in the absence of overflow or underflow. In this paper, we propose a new fast implementation of the second barycentric formula for higher order Hermite--...

We propose three time-splitting schemes for nonlinear time-fractional differential equations with smooth solutions, where the order of the fractional derivative is $0<\alpha<1$. While one of the schemes is of order $\alpha$, the other two schemes are of ...

Continuum-time random walk is a general model for particle kinetics, which allows for incorporating waiting times and/or non-Gaussian jump distributions with divergent second moments to account for Lévy flights. Exponentially tempering the probability ...

We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible ...

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high-order weighted essentially nonoscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high-order positivity-...

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We formulate a ...

We propose an adaptive Wick--Malliavin (WM) expansion in terms of the Malliavin derivative of order $Q$ to simplify the propagator of general polynomial chaos (gPC) of order $P$ (a system of deterministic equations for the coefficients of gPC) and to ...

Our purpose is to analyze mixed continuous and discontinuous Galerkin discretizations of the time harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. Under appropriate ...

A family of $C^\infty$ compactly supported radial kernels is presented. These positive definite kernels can be generated numerically using convolutions of compactly supported radial functions. An alternative proof that shows the infinitely smooth limit ...

A method is presented to generate surface boundary layers. The novelty of the method consists in a uniform treatment of the concave and convex regions based on offsetting the initial front. In particular, concave situations are enforced to respect the ...

The ensemble density functional theory (E-DFT) is valuable for simulations of metallic systems due to the absence of a gap in the spectrum of the Hamiltonian matrices. Although the widely used self-consistent field (SCF) iteration method can be extended to ...

We consider the linear time-dependent Schrödinger equation with a time-dependent smooth potential on an unbounded domain. A Galerkin spectral method with a tensor-product Hermite basis is used as a discretization in space. Discretizing the resulting ODE ...

Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find starting points that ...

In this paper, we first show that the second-order cone linear complementarity problem (SOCLCP) can be solved by finding a positive zero $s_*\in \mathbb{R}$ of a particular rational function $h(s)$, and we then propose a Krylov subspace method to reduce $h(s)...

A constant mean curvature (CMC) surface is a critical point of surface area with respect to variations that preserve the volume bounded by the surface. We present a simple and elegant method for constructing a triangle mesh approximation to a CMC surface by ...

The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows us to characterize the convergence of this method in terms of the error ...

This work presents a nonlinear model reduction approach for systems of equations stemming from the discretization of partial differential equations with nonlinear terms. Our approach constructs a reduced system with proper orthogonal decomposition and the ...

Dense particulate flow simulations using integral equation methods demand accurate evaluation of Stokes layer potentials on arbitrarily close interfaces. In this paper, we generalize techniques for close evaluation of Laplace double-layer potentials in [J. ...

In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major ...

The estimation of neuronal activity in the human brain from electroencephalography (EEG) and magnetoencephalography (MEG) signals is a typical inverse problem whose solution process requires an accurate and fast forward solver. In this paper the method of ...

Multiphase viscous flow is usually modeled by a coupled system of differential equations comprising hyperbolic partial differential equations describing the evolution of the volume fraction of each phase and elliptic partial differential equations ...

In this article, we derive a semi-Lagrangian scheme for the solution of the Vlasov equation represented as a low-parametric tensor. Grid-based methods for the Vlasov equation have been shown to give accurate results but their use has mostly been limited ...

The quasi-static brittle fracture model proposed by G. Francfort and J.-J. Marigo can be $\Gamma$-approximated at each time evolution step by the Ambrosio--Tortorelli functional. In this paper, we focus on a modification of this functional which ...

We develop computational methods for the simulation of osmotic swelling phenomena relevant to microscopic vesicles containing transformable solute molecules. We introduce stochastic immersed boundary methods (SIBMs) that can capture osmotically driven ...

The importance of stencil-based algorithms in computational science has focused attention on optimized parallel implementations for multilevel cache-based processors. Temporal blocking schemes leverage the large bandwidth and low latency of caches to ...

We present the design of an object oriented general purpose library for isogeometric analysis, where the mathematical concepts of the isogeometric method and their relationships are directly mapped into classes and their interactions. The encapsulation of ...