Related papers: A non-balanced staggered-grid finite-difference sc…
In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of…
In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced and analyzed. This…
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and…
We design a conservative finite difference scheme for ideal magnetohydrodynamic simulations that attains high-order accuracy, shock-capturing, and divergence-free condition of the magnetic field. The scheme interpolates pointwise physical…
This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties…
Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
Phase field models are promising to tackle various fracture problems where a diffusive crack is introduced and modelled using the phase variable. Owing to the non-convexity of the energy functional, the derived partial differential…
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…
A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…