Computational multiscale methods for first-order wave equation using mixed CEM-GMsFEM

Generalized Multiscale Finite Element Methods (GMsFEM)

Article history: Received 8 September 2012 Received in revised form 18 April 2013 Accepted 24 April 2013 Available online 22 May 2013

A method for solving first order fuzzy differential equation

Tailored Finite Point Method for First Order Wave Equation

Following the idea of the tailored finite point method proposed in [2, 7], a series of efficient numerical schemes are developed for the one dimensional scalar wave equation within various types of media. Stability and accuracy are analyzed and numerically verified. In particular we can obtain unconditionally stable implicit schemes that can be solved explicitly for boundary value problems. We ...

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on ...

High-order methods for computational wave propagation and scattering

This workshop was concerned with the development of numerical methods for wave propagation with a focus on high-order convergence for general scattering configurations (with applicability to complex and singular geometries and high frequency problems), including integral equations, finite-difference and finite-element algorithms, spectral and Fourier based approaches and hybrids of asymptotic a...