Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales

Details Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales

2006-04-18

arxiv.org/abs/math/0604380v3

Mathematics

Numerical Analysis

27 pages, 4 figures, Submitted

Scientific paper

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 $L^2$ (instead $H^{-1}$ with respect to Euclidean coordinates) and the solution itself is in $L^{\infty}(0,T,H^2(\Omega))$ (instead of $L^{\infty}(0,T,H^1(\Omega))$ 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.

Affiliated with

Also associated with

No associations

Rating

Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-195593