A first implementation of a optimal adaptive algorithm for elliptic
operator equations.
Arne Barinka, Titus Barsch, Philippe Charton,
Albert Cohen, Wolfgang
Dahmen, Stephen Dahlke, Karsten Urban
16 Septembre 1998
The goal of the project we have been working on during this CEMRACS, is to
implement the algorithm proposed by Albert Cohen, Wolfgang Dahmen and Ronald De
Vore in an incoming paper "Adaptive Wavelet Methods for Elliptic Operator
Equations - Convergence Rates".
The key point of this algorithm is the way to apply a quasi-sparse matrix to
a sparse vector, based on a decomposition of the vector and the matrix.
We have made a first implementation in C++ of this algorithm and have done some
tests for 1D problem.
We want to continue this project in several directions :
- actually the computation of the stiffness matrix of the problem is done
on a finest scale, we want to compute only needed coefficients and by this
way avoid the problem of choosing a priori a finest scale,
- we also want to optimize the matrix-vector product used in the conjugate
gradient algorithm on which the result coefficients set to be computed is
known before the computation.
- Then, we have planed to do some tests in 2D.
The continuation of this project is needing, at least, an other meeting of the
team.