SIAM Journal on Scientific Computing

We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance, and transmission boundary conditions. In particular, we aim to quantify diffracted fields originated by small ...

The main contribution of this paper is twofold: On the one hand, a general framework for performing Hermite interpolation on Riemannian manifolds is presented. The method is applicable if algorithms for the associated Riemannian exponential and logarithm ...

We develop novel stabilized cut discontinuous Galerkin methods for advection-reaction problems. The domain of interest is embedded into a structured, unfitted background mesh in $\mathbb{R}^d$ where the domain boundary can cut through the mesh in an ...

A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in the multigrid method, solving the eigenvalue problem in the finest space is decomposed into ...

This paper deals with a strategy to solve numerically control problems of the Stackelberg--Nash kind for heat equations with Dirichlet boundary conditions. We assume that we can act on the system through several controls, respecting an order and a ...

Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both internode communications and even moreso in intranode data motion. A new approach to address this limitation is to make use of data ...

Inspired by recent developments in multilevel Monte Carlo (MLMC) methods and randomized sketching for linear algebra problems, we propose an MLMC estimator for real-time processing of matrix structured random data. Our algorithm is particularly effective ...

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth tracking-type ...

The time parallel solution of optimality systems arising in PDE constrained optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the optimization ...

This work presents a model reduction approach for problems with coherent structures that propagate over time, such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these transport-dominated ...

This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via interpolation in ...

We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multisymplectic partial differential equations with cubic invariants. The methods are tested on the one-dimensional Korteweg--de ...

The stochastic weighted particle method (SWPM) is a Monte Carlo technique developed by Rjasanow and Wagner that generalizes Bird's direct simulation Monte Carlo method for solving the Boltzmann equation. To reduce computational cost due to the gradual ...

We develop efficient algorithms for computing the multidimensional fractional operator $( -\Delta_{x})^{\frac{\alpha}{2}}$ in the form of hypersingular integral in the entire space, where the operator is the so-called integral fractional Laplacian when $0 ...

In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for linear hyperbolic equations [W. Guo and Y. Cheng, SIAM J. Sci. Comput., 38 (...

We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In contrast to existing techniques, our method does not rely on detailed ...

Approximations of functions with finite data often do not respect certain “structural” properties of the functions. For example, if a given function is nonnegative, a polynomial approximation of the function is not necessarily also nonnegative. We propose ...

In this paper, we present a novel numerical method that redistributes unevenly given points on an evolving closed curve to satisfy equi-arclength(-like) condition. Without substantial difficulty, it is also capable of remeshing or employing adaptive mesh ...

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on finite element method--spectral element method (FEM-SEM) equivalence and additive ...

The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we study conjugate gradient variants ...

Solution interpolation between deforming meshes is an important component for several applications in scientific computing, including indirect arbitrary-Lagrangian-Eulerian and rezoning moving mesh methods in numerical solution of PDEs. In this paper, a high-...

This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The well-known ...

Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the AAA-Lawson algorithm, ...

We define a new two-level optimized Schwarz method (OSM), and we provide a convergence analysis both for overlapping and nonoverlapping decompositions. The two-level analysis suggests how to choose the optimized parameters. We also discuss an optimization ...

Recently, there has been interest in high precision approximations of the first eigenvalue of the Laplace--Beltrami operator on spherical triangles for combinatorial purposes. We compute improved and certified enclosures to these eigenvalues. This is ...

We explore the computational issues concerning a new algorithm for the classical least-squares approximation of $N$ samples by an algebraic polynomial of degree at most $n$ when the number $N$ of the samples is very large. The algorithm is based on a ...

This paper proposes a new computational method for solving the structured least squares problem that arises in the process of identification of coherent structures in dynamic processes, such as, e.g., fluid flows. It is deployed in combination with dynamic ...

In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common deep neural ...

We study for the first time Schwarz domain decomposition methods for the solution of the Navier equations modeling the propagation of elastic waves. These equations in the time-harmonic regime are difficult to solve by iterative methods, even more so than ...

We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport distance over graph ...