An Chen^*

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.1, pp. 173-195, 2020, DOI:10.32604/cmes.2020.011871 - 18 September 2020

Abstract In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time. More >

Yuan Li¹, Jianming Zhang^1,2, Guizhong Xie¹, Xingshuai Zheng¹, Shuaiping Guo¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 187-206, 2014, DOI:10.3970/cmes.2014.101.187

Abstract In this paper, a time-domain boundary element method formulation for the analysis of three-dimensional elastodynamic problems with arbitrary, non-null initial conditions is presented. The formulation is based on the convolution quadrature method, by which the numerical stability is improved significantly. In order to take into account the non-null initial conditions in this formulation, a general method is developed to replace the initial conditions by equivalent pseudo-forces based on the pseudo-force method. The original governing equation is transformed into a new one subjected to null initial conditions. In the numerical examples, longitudinal vibrations of a free More >

M. Schanz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 109-130, 2010, DOI:10.3970/cmes.2010.058.109

Abstract Boundary Element formulations in time domain suffer from two problems. First, for hyperbolic problems not too much fundamental solutions are available and, second, the time stepping procedure is expensive in storage and has stability problems for badly chosen time step sizes. The first problem can be overcome by using the Convolution Quadrature Method (CQM) for time discretisation. This as well improves the stability. However, still the storage requirements are large. A recently published reformulation of the CQM by Banjai and Sauter [Rapid solution of the wave equation in unbounded domains, SIAM J. Numer. Anal., 47,… More >

A.I. Abreu¹, W.J. Mansur¹, D. Soares Jr^1,2, J.A.M. Carrer³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 123-132, 2008, DOI:10.3970/cmes.2008.030.123

Abstract This paper is concerned with the numerical computation of space derivatives of a time-domain (TD-) Boundary Element Method (BEM) formulation for the analysis of scalar wave propagation problems. In the present formulation, the Convolution Quadrature Method (CQM) is adopted, i.e., the basic integral equation of the TD-BEM is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multi-step method. In order to numerically compute space derivatives, the present work properly transforms the quadrature weights of the CQM-BEM, adopting the so-called Complex-Variable-Differentiation Method (CVDM). More >