Journal of Scientific Computing

We introduce and analyze a hybridizable discontinuous Galerkin (HDG) approach for the strongly damped linear wave equation. In our investigation, we derive a priori error estimates to demonstrate the optimal convergence of the approximations for ...$\mathrm{}$$\mathrm{}$${\mathrm{}}^{\mathrm{}}{}^{\mathrm{}}$

We develop a general theoretical and algorithmic framework for sparse approximation and structured prediction in ${\mathcal{P}}_2(\Omega )$ with Wasserstein barycenters. The barycenters are sparse in the sense that they are computed from an available dictionary of ...

We consider the geometric inverse problem of determining an immersed obstacle in a 2D linear wave equation from overspecified boundary data. We use the topological gradient method to solve this problem. The unknown obstacle is reconstructed using ...

In this paper, based on Mann-type and Halpern-type algorithms, we introduce two modified extragradient algorithms with novel stepsize rules and inertial technique for solving pseudo-monotone variational inequality problems in Hilbert and reflexive ...

In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular domains via semigroup theory and computer-assisted proofs. Once a ...

Measurements of light typically capture amplitude information, often overlooking crucial phase details. This oversight underscores the importance of phase retrieval (PR), essential in biomedical imaging, X-ray crystallography, and microscopy, for ...

We present and analyze a new hybridizable discontinuous Galerkin method for the Reissner–Mindlin plate bending problem. Our method is based on the formulation utilizing Helmholtz Decomposition. Then the system is decomposed into three problems: ...

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired data or ...

In this paper we consider adaptive deep neural network approximation for stochastic dynamical systems. Based on the continuity equation associated with the stochastic dynamical systems, a new temporal KRnet (tKRnet) is proposed to approximate the ...

Image alignment is an important problem in computer vision, which can be solved by tensor based methods that are robust to noise and have satisfactory performance. However, these methods face two common challenges: (1) they have high computational ...

This paper investigates polynomial chaos methods for the linear parabolic stochastic partial differential equations (SPDEs) driven by a special type of colored noises, i.e., the Ornstein–Uhlenbeck (OU) noise. Unlike the study for the SPDEs driven ...

In this paper, we develop a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems. First, a differentiable augmented Lagrangian (AL) function is constructed by utilizing the ...

This paper is concerned with the fast algorithm for solving multidimensional spatial fractional Cahn-Hilliard equations. The equations are discretized by a linear and energy-stable finite difference scheme. It gives a system of linear equations ...$\mathrm{}\mathrm{}$$\frac{\mathrm{}}{\mathrm{}}\frac{\mathrm{}}{\mathrm{}\sqrt{\mathrm{}}}\frac{\mathrm{}}{\mathrm{}\sqrt{\mathrm{}}}\frac{\mathrm{}}{\mathrm{}}$

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating ${\ell }_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our algorithm ...