Solution of biharmonic equations with application to radar imaging
This paper is concerned with the mathematical inverse problem to be resolved in order to recover the ground topography height function from radar data. It is proved that this problem amounts to solve Poisson's equation with the following difficulties: -- the solution has to be looked over a very large rectangular grid; -- boundary values are not known. To obtain suitable solutions, the authors propose two different methods. Both methods consist to introduce a minimizing criterion involving Sobolev norms of the solution; in this way, they propose two possible choices of criteria. In both cases, they prove that these formulations amount to solve biharmonic problems with appropriate boundary data. Then, fast numerical techniques are investigated to solve these biharmonic problems. Finally, some numerical experiments prove the efficiency of such methods. This is a very nice paper giving very well analyzed and powerful methods to solve difficult and important technical problems.
scientific article; zbMATH DE number 1326545