Abstract Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system time-domain boundary integral equations and the second order formulation wave equation described. fully discrete consists spatial discretization finite element methods (BEM/FEM), leapfrog time-stepping interior, convolution quadrature for equations. Convo...

The finite element method (FEM) is a well known numerical method in solving partial differential equations (PDEs). All numerical methods inherently have error in comparison to the true solution of the PDE. Base on the FEM theory, the appropriate norm of this error is bounded and it can be estimated by the mesh size. One standard method to get an idea about the sensibility of the numerical solut...

Experiments of crack propagation in rubbers have shown that a discontinuous jump of crack propagation velocity can occur as energy release rate increases, which is known as the "mode transition" phenomenon. Although it is believed that the mode transition is strongly related to the mechanical properties, the nature of the mode transition had not been revealed. In this study, dynamic crack propa...

The finite element method (FEM) is well suited for use in the non-rigid registration of magnetic resonance spectroscopy images (MRSI) with intraoperative ultrasound images of the prostate because FEM provides a principled method for modeling the physical deformation caused when the MRSI intra-rectal imaging probe compresses the prostate. However, FEM requires significant labor and computational...

We present a new class of adaptivity algorithms for time-dependent partial differential equations (PDE) that combines adaptive higher-order finite elements (hp-FEM) in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time. Weak formulation is only created for the stationary residual of the equation, and the Runge-Kutta method is supplied via its Butcher’s table. Ar...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

This paper introduces a parallel algorithm for the scaled boundary finite element method (SBFEM). The application code is designed to run on clusters of computers, and it enables the analysis of large-scale soil-structure-interaction problems, where an unbounded domain has to fulfill the radiation condition for wave propagation to infinity. The main focus of the paper is on the mathematical des...