SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2943-A2973, January 2020. 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 (2016), pp. A3381--A3409, W. Guo and Y. Cheng, SIAM J.

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2910-A2942, January 2020. 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 $0 < \alpha < 2$. By introducing polar coordinates, we reduce

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2889-A2909, January 2020. 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 increase in the number of stochastic particles in the SWPM

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page B1173-B1192, January 2020. We propose a new numerical method to solve the linearized problem of the travel time tomography with incomplete data. Our method is based on the technique of the truncation of the Fourier series with respect to a special basis of $L^{2}$. This way we derive a boundary value problem for a system of coupled PDEs

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2865-A2888, January 2020. 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 Vries equation and the two-dimensional Zakharov--Kuznetsov

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page C265-C293, January 2020. In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and Hermitian, and $S$ is positive definite. This type of matrix emerges from the representation

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2837-A2864, January 2020. 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 low-dimensional spaces. It has been observed that empirical

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2803-A2836, January 2020. 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 problems because propagating coherent structures typically

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page C245-C264, January 2020. Multidimensional discrete Fourier transforms (DFTs) are typically decomposed into multiple one-dimensional (1D) transforms. Hence, parallel implementations of any multidimentional DFT focus on parallelizing within or across the 1D DFT. Existing DFT packages exploit the inherent parallelism across the 1D DFTs and

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2773-A2802, January 2020. 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 loop. We propose here a different strategy by devising directly

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page C221-C244, January 2020. Almost all efforts to optimize high-performance matrix-matrix multiplication have been focused on the case where matrices contain real elements. The community's collective assumption appears to have been that the techniques and methods developed for the real domain carry over directly to the complex domain. As a

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page B1136-B1172, January 2020. A new well-balanced asymptotic preserving scheme for two-dimensional low Froude number shallow water flows over irregular bottom is developed in this study. The bed-slope terms in the low Froude number regime are nontrivial since their stiffness has the same order as the gravity waves, they change the flow behavior

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2750-A2772, January 2020. 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 functional subject to a linear partial differential equation

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2731-A2749, January 2020. 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 in handling high-dimensional inner products and matrix multiplication

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2701-A2730, January 2020. 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 compression in the form of a compressed data array. Storing

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2678-A2700, January 2020. 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 hierarchy: a first control (the leader) is assumed to choose the

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2655-A2677, January 2020. 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 solving the standard linear boundary value problems and very-low-dimensional

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2620-A2654, January 2020. 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 arbitrary fashion. To cope with robustness problems caused by

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page C193-C220, January 2020. The multigroup neutron transport equation is crucial for studying the motion of neutrons and their interaction with materials. Numerical simulation of the multigroup neutron transport equation is computationally challenging because the equation is defined on a high-dimensional phase space, the computational spatial

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2593-A2619, January 2020. 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 mappings are available. This includes many of the matrix

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page B1115-B1135, January 2020. We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2561-A2592, January 2020. 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 stochastic perturbations of a given relatively smooth nominal

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2537-A2560, January 2020. In this paper, we introduce staggered discontinuous Galerkin methods for the stationary Stokes flow on polygonal meshes. The proposed method is based on the pseudostress-velocity formulation. A Lagrange multiplier on dual edges is introduced to impose the continuity of the pseudostress, which reduces the size

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2514-A2536, January 2020. We present several essential improvements to the powerful scalar auxiliary variable (SAV) approach. Firstly, by using the introduced scalar variable to control both the nonlinear and the explicit linear terms, we are able to reduce the number of linear equations with constant coefficients to be solved at each

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2489-A2513, January 2020. We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the scalar auxiliary variable (SAV) approach combined with the Lagrangian multiplier approach. They are as efficient as the SAV schemes for unconstrained gradient

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2461-A2488, January 2020. Nonlinear domain decomposition (DD) methods, such as ASPIN (additive Schwarz preconditioned inexact Newton), RASPEN (restricted additive Schwarz preconditioned inexact Newton), nonlinear FETI-DP (finite element tearing and interconnecting-dual primal), and nonlinear BDDC (balancing DD by constraints), can be reasonable

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B1092-B1114, January 2020. Structural optimization searches for the optimal shape and topology of components such that specific physical quantities are optimized, for instance, the stability of the resulting structure. Problems involving multiple scales, i.e., structures on a microscopic and a macroscopic level, can be efficiently solved

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2436-A2460, January 2020. We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2402-A2435, January 2020. We consider the development of high-order space and time numerical methods based on implicit-explicit multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which the convection and the source term may have very different time and space scales

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page C169-C191, January 2020. A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine precision by using a three-dimensional analogue of the double Fourier sphere

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2371-A2401, January 2020. We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds $\mathbb{M} \subset \mathbb{R}^3$ of codimension 1. Our technique involves automatic addition of artificial hyperviscosity to damp

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B1067-B1091, January 2020. We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier--Stokes equations, using the discontinuous Galerkin method as deterministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes while simultaneously increasing the

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2360-A2370, January 2020. The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a nonlinear problem. By first replacing the original global PDE with the Schwarz

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B1041-B1066, January 2020. Anisotropic elliptic interface problems are important but hard to solve either analytically or numerically. There is limited literature on numerical methods based on structured meshes. Finite element methods are often used, but the usual average error estimates cannot guarantee accuracy of the solution near or

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2344-A2359, January 2020. We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [T. Aslam, J. Comput. Phys., 193 (2004), pp. 349--355], in which normal derivatives are extrapolated, the proposed approach

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page C143-C168, January 2020. We design and implement an efficient parallel algorithm for finding a perfect matching in a weighted bipartite graph such that weights on the edges of the matching are large. This problem differs from the maximum weight matching problem, for which scalable approximation algorithms are known. It is primarily motivated

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2325-A2343, January 2020. The inverse acoustic scattering of point objects using multifrequency sparse measurements is studied. The objects may be a sum of point sources or point-like scatterers. We show that the locations and scattering strengths of the point objects can be uniquely identified by the multifrequency near or far fields

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B1014-B1040, January 2020. For both isothermal and thermal petroleum reservoir simulation, the constrained pressure residual (CPR) method is the industry-standard preconditioner. This method is a two-stage process involving the solution of a restricted pressure system. While initially designed for the isothermal case, CPR is also the standard

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B983-B1013, January 2020. The computation of the ground states of spin-$F$ Bose--Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier pseudospectral schemes and view the discretized problem as an optimization

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B951-B982, January 2020. The purpose of this article is to propose and analyze a new coupled multiphysics model and a decoupled stabilized finite element method for the closed-loop geothermal system, which mainly consists of a network of underground heat exchange pipelines to extract the geothermal heat from the geothermal reservoir. The

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2300-A2324, January 2020. We devise and analyze a hybrid high-order (HHO) method to discretize unilateral and bilateral contact problems with Tresca friction in small strain elasticity. The nonlinear frictional contact conditions are enforced weakly by means of a consistent Nitsche technique with symmetric, incomplete, and skew-symmetric

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2281-A2299, January 2020. A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the input data and then convolving the interpolant with a multiresolution Gaussian

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2262-A2280, January 2020. We propose and study a new multivariate stochastic scattered data quasi-interpolation scheme that is reminiscent of the classical Monte Carlo method for estimating integrals. We first employ a convolution operator to approximate (deterministically) Sobolev space functions and use a result of Cheney, Light, and

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2230-A2261, January 2020. This paper presents entropy symmetrization and high-order accurate entropy stable schemes for the relativistic magnetohydrodynamic (RMHD) equations. It is shown that the conservative RMHD equations are not symmetrizable and do not admit a thermodynamic entropy pair. To address this issue, a symmetrizable RMHD

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B921-B950, January 2020. The approximate Riemann solver of Harten--Lax--van Leer (HLL) and its variant HLLC (HLL with Contact restoration) solver are widely used as flux functions of finite volume Godunov-type methods for the solution of the gas dynamic Euler equations. However, the HLLC solver suffers from two significant difficulties:

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2206-A2229, January 2020. We develop a new moving-water equilibria preserving numerical scheme for the Saint-Venant system. The new scheme is designed in two major steps. First, the geometric source term is incorporated into the discharge flux, which results in a hyperbolic system with a global flux. Second, the discharge equation is relaxed

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2182-A2205, January 2020. We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies by forming low-rank approximations to the sought after solution at selected timesteps.

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2158-A2181, January 2020. We develop a new numerical method, namely, a locking-free staggered cell-centered discontinuous Galerkin method for linear elasticity on fairly general meshes. The method is well suited for general meshes possibly including hanging nodes; in particular, it does not deteriorate when the mesh becomes highly distorted

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2134-A2157, January 2020. We consider the problem of optimizing an unknown function over a multidimensional continuous domain, where function evaluation is noisy and expensive. We assume that a globally accurate model of the function is not available, but there exist some parametric models that can well approximate the function in local

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2108-A2133, January 2020. The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. We propose an extension of the framework introduced in [D. A. Bini, S. Massei, and B. Meini, Math. Comp., 87

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2088-A2107, January 2020. This paper deals with the 3/4-discrete 2-Wasserstein optimal transport between two measures, where one is supported on a set of line segments and the other is supported on a set of points. We select the most suitable optimization procedure that computes the optimal transport. Then we address the problem of projecting

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2062-A2087, January 2020. The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial differential equation (PDE). Since numerical evaluations of PDEs are computationally

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B894-B920, January 2020. In this paper we consider wave propagation problems in two-dimensional unbounded domains, including dissipative effects, reformulated in terms of space-time boundary integral equations. For their solution, we employ a convolution quadrature (CQ) for the temporal and a Galerkin boundary element method (BEM) for the

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2037-A2061, January 2020. In the last few years, several methods have been developed to deal with jump singularities in parametric or stochastic hyperbolic PDEs. They typically use some alignment of the jump-sets in physical space before performing well-established reduced order modeling techniques such as reduced basis methods, proper

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2014-A2036, January 2020. In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple perturbed problems by reusing local computations performed with the reference

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A1984-A2013, January 2020. A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of total variation. On the other hand, sparse or noisy data often demand a probabilistic approach to the reconstruction of images, to enable uncertainty quantification;

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B869-B893, January 2020. The discrete ordinates discontinuous Galerkin ($S_N$-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind $S_N$-DG method. The proposed method uses a smaller finite element space that is constructed by coupling

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B847-B868, January 2020. The immersed boundary (IB) method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto immersed structures. To resolve slender fibers, the grid spacing must be

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A1950-A1983, January 2020. A new iterative method, the WaveHoltz iteration, for solution of the Helmholtz equation is presented. WaveHoltz is a fixed point iteration that filters the solution to the solution of a wave equation with time periodic forcing and boundary data. The WaveHoltz iteration corresponds to a linear and coercive operator

SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A1935-A1949, January 2020. Nonlocal models provide exceptional simulation fidelity for a broad spectrum of scientific and engineering applications. However, wider deployment of nonlocal models is hindered by several modeling and numerical challenges. Among those, we focus on the nontrivial prescription of nonlocal boundary conditions, or