Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4636255 | Applied Mathematics and Computation | 2007 | 12 Pages |
Abstract
It is known that the ith order laminated microstructures can be resolved by the kth order rank-one convex envelopes with k ⩾ i. So the requirement of establishing an efficient numerical scheme for the computation of the finite order rank-one convex envelopes arises. In this paper, we develop an iterative scheme for such a purpose. The first order rank-one convex envelope R1f is approximated by evaluating its value on matrixes at each grid point in Rmn and then extend to non-grid points by interpolation. The approximate kth order rank-one convex envelope Rkf is obtained iteratively by computing the approximate first order rank-one convex envelope of the numerical approximation of Rkâ1f. Compared with O(h1/3) obtained so far for other methods, the optimal convergence rate O(h) is established for our scheme, and numerical examples illustrate the computational efficiency of the scheme.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xin Wang, Zhiping Li,