A new adaptive Fundamental Solution Method (FSM) for the approximate solution of scalar elliptic boundary value problems is presented. The construction of the basis functions is based on the Adaptive Cross Approximation (ACA) of the fundamental solution of the corresponding elliptic operator. An algorithm for an immediate computer implementation of the method is formulated. A series of numerica...

Developing robust and ecient numerical solution methods for Richards' equation (RE) continues to be a challenge for certain problems. We consider such a problem here: in®ltration into unsaturated porous media initially at static conditions for uniform and non-uniform pore size media. For ponded boundary conditions, a sharp in®ltration front results, which propagates through the media. We evalu...

In this paper, we give a survey on the three main aspects of the ee-cient treatment of PDEs, i.e. adaptive discretization, multilevel solution and par-allelization. We emphasize the abstract approach of subspace correction schemes and summarize its convergence theory. Then, we give the main features of each of the three distinct topics and treat the historical background and modern developments...

Wavelets and radial basis functions (RBF) have ubiquitously proved very successful to solve different forms of partial differential equations (PDE) using shifted basis functions, and as with the other meshless methods, they have been extensively used in scattered data interpolation. The current paper proposes a framework that successfully reconciles RBF and adaptive wavelet method to solve the ...