Journal of Scientific Computing

We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can also ...

We present a new high-order spectral element solution to the two-dimensional scalar Poisson equation subject to a general Robin boundary condition. The solution is based on a simplified version of the shifted boundary method employing a continuous ...

We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and ...

In this work, we extend recent research on the fully mixed virtual element method based on Banach spaces for the stationary Boussinesq equation to suggest and analyze a new mixed-virtual element technique for the stationary generalized Boussinesq ...$\mathbb{}{\mathbf{}}_{\mathrm{}\mathrm{}}$$\mathbf{}{}_{\mathrm{}\mathrm{}}$

This paper proposes and investigates the two-grid stabilized lowest equal-order finite element method for the time-independent dual-permeability-Stokes model with the Beavers-Joseph-Saffman-Jones interface conditions. This method is mainly based ...${}_{\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}}$${}^{\mathrm{}}$

In this paper, we investigate the sharpness of a Korn’s inequality for piecewise $H^1$ space and its applications. We first revisit a Korn’s inequality for the piecewise $H^1$ space based on general polygonal or polyhedral decompositions of the domain. ...

In this paper, we consider numerical approximations for the optimal partition problem using Lagrange multipliers. By rewriting it into constrained gradient flows, three and four steps numerical schemes based on the Lagrange multiplier approach are ...

Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical technique ...

A dynamic mesh approach for conservation laws has been developed to compute discontinuities with high accuracy. The basic idea is to move the mesh interface at the speed of discontinuity at that interface. For any 1D scalar conservation law with ...

In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term induced by ...

In this paper, a fifth-order moment-based Hermite weighted essentially non-oscillatory scheme with unified stencils (termed as HWENO-U) is proposed for hyperbolic conservation laws. The main idea of the HWENO-U scheme is to modify the first-order ...

We present a new second order accurate structure-preserving finite volume scheme for the solution of the compressible isentropic two-phase model of Romenski et. al (Romenski J Sci Comput. 42, 68-95 2010), Romenski Q Appl Math 65(2), 259-279 2007) ...

Non-backtracking PageRank is a variation of Google’s PageRank, which is based on non-backtracking random walk. However, if the number of dangling nodes of a graph is large, the non-backtracking PageRank algorithm proposed in [F. Arrigo, D. Higham, ...

This paper presents a reduced projection method for the solution of quasiperiodic Schrödinger eigenvalue problems for photonic moiré lattices. Using the properties of the Schrödinger operator in higher-dimensional space via a projection matrix, we ...

Linear inverse problems arise in many practical applications. In the present work, we propose a residual-based surrogate hyperplane Bregman-Kaczmarz method (RSHBK) for solving this kind of problems. The convergence theory of the proposed method is ...

In this paper, we present and analyze a weighted residual a posteriori error estimate for a sparse optimal control problem. The problem involves a non-differentiable cost functional, a state equation with an integral fractional Laplacian, and ...${}^{\mathrm{}}$

This paper introduces and analyzes a staggered discontinuous Galerkin (DG) method for quasi-Newtonian Stokes flow problems on polytopal meshes. The method introduces the flux and tensor gradient of the velocity as additional unknowns and ...

Considered herein is a class of Boussinesq systems of Bona–Smith type that describe the propagation of long surface water waves of small amplitude in bounded two-dimensional domains with slip-wall boundary conditions and variable bottom ...

In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-r polynomials and face unknowns represented by degree-s polynomials, ...$\mathrm{}$

Conventional wisdom suggests that high-order finite-difference methods are more efficient than high-order discontinuous spectral-element methods on smooth meshes, but less efficient as the mesh becomes increasingly distorted because of a ...

In this paper, we propose a Nitsche’s extended conforming virtual element method, which combines the Nitsche’s extended finite element method with the conforming virtual element method, for solving stokes interface problems with the unfitted-...

In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use energy ...${}^{\mathrm{}}$${}^{\mathrm{}\mathrm{}}$${}^{\mathrm{}\mathrm{}}$${}^{\mathrm{}}$

In the field of machine learning, many large-scale optimization problems can be decomposed into the sum of two functions: a smooth function and a nonsmooth function with a simple proximal mapping. In light of this, our paper introduces a novel ...

This paper introduces a nonconvex approach for sparse signal recovery, proposing a novel model termed the ${\tau }_2$-model, which utilizes the squared ${\ell }_1/{\ell }_2$ norms for this purpose. Our model offers an advancement over the ${\ell }_0$ norm, which is often ...${}_{\mathrm{}}$

A Lawson-type exponential integrator combined with the Fourier pseudo-spectral method is provided for the nonlinear Double Sine-Gordon equation (DSGE), while the nonlinearity is characterized by $\beta /ϵ$ with small parameter $ϵ\in (0,1]$ and interaction ...$\mathrm{}$${}^{\mathrm{}}{}^{}$${}_{}{}^{\mathrm{}}$$$$\mathrm{}$$$$\mathrm{}\mathrm{}$${}^{\mathrm{}}$${}^{\mathrm{}}{}^{\mathrm{}}$

Isogeometric analysis (IGA) has been widely used as a spatial discretization method for phase field models since the seminal work of Gómez et al. (Comput. Methods Appl. Mech. Engrg. 197(49), pp. 4333–4352, 2008), and the first numerical ...${}^{}$