کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
499343 | 863041 | 2008 | 10 صفحه PDF | دانلود رایگان |
In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded. We show that under a Cordes type condition the second order derivatives of the solution with respect to harmonic coordinates are L2L2 (instead H-1H-1 with respect to Euclidean coordinates) and the solution itself is in L∞(0,T,H2(Ω))L∞(0,T,H2(Ω)) (instead of L∞(0,T,H1(Ω))L∞(0,T,H1(Ω)) with respect to Euclidean coordinates). Then, we propose an implicit time stepping method to solve the resulted linear system on coarse spatial scales, and present error estimates of the method. It follows that by pre-computing the associated harmonic coordinates, it is possible to numerically homogenize the wave equation without assumptions of scale separation or ergodicity.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 198, Issues 3–4, 15 December 2008, Pages 397–406