Space - time BIE methods for non homogeneous exterior wave equation problems . The Dirichlet case . ∗
نویسندگان
چکیده
In this paper we consider the (2D and 3D) exterior problem for the non homogeneous wave equation, with a Dirichlet boundary condition and non homogeneous initial conditions. First we derive two alternative boundary integral equation formulations to solve the problem. Then we propose a numerical approach for the computation of the extra “volume” integrals generated by the initial data. Finally, to show the efficiency of this approach, we solve some test problems by applying a second order Lubich discrete convolution quadrature for the discretization of the time integral, coupled with a collocation first, and a Galerkin then, boundary element method.
منابع مشابه
Exact Nonreflecting Boundary Conditions for Exterior Wave Equation Problems
We consider the classical wave equation problem defined on the exterior of a bounded 2D space domain, possibly having far field sources. We consider this problem in the time domain, but also in the frequency domain. For its solution we propose to associate with it a boundary integral equation (BIE) defined on an artificial boundary surrounding the region of interest. This boundary condition is ...
متن کاملEnergetic Bem for the Numerical Solution of Damped Wave Propagation Exterior Problems
The analysis of damping phenomena that occur in many physics and engineering problems, such as fluid dynamics, kinetic theory and semiconductors, is of particular interest. For this kind of problems, one needs accurate and stable approximate solutions even on large time intervals. These latter can be obtained reformulating time-dependent problems modeled by partial differential equations (PDEs)...
متن کاملPotential evaluation in space-time BIE formulations of 2D wave equation problems
In this paper we examine the computation of the potential generated by space-time BIE representations associated with Dirichlet and Neumann problems for the 2D wave equation. In particular, we consider the efficient evaluation of the (convolution) time integral that appears in the potential representation. For this, we propose two simple quadrature rules which appear more efficient than the cur...
متن کاملRheological Response and Validity of Viscoelastic Model Through Propagation of Harmonic Wave in Non-Homogeneous Viscoelastic Rods
This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest....
متن کاملInvestigation of the Effects of Non-Linear and Non-Homogeneous Non-Fourier Heat Conduction Equations on Temperature Distribution in a Semi-Infinite Body
In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...
متن کامل