Abstract: This paper presents the first results to combine two theoretically sound methods (spectral projection and multigrid methods) together to attack ill-conditioned linear systems. Our preliminary results show that the proposed algorithm applied to a Krylov subspace method takes much fewer iterations for solving an ill-conditioned problem downloaded from a popular online sparse matrix collection.

Abstract: We discuss decoupling issues in multi-physics and complex system computation. A general framework is presented for decoupling coupled PDE models in multi-physics applications. Examples of decoupled numerical algorithms and theory are illustrated for two-grid/multi-grid methods, preconditioning methods, mixed implicit/explicit marching methods for coupled fluid/porous media flows, fluid-solid interaction, superconductivity, etc

Abstract: Due the recent increase of the volume of data that has been generated, organizing this data has become one of the biggest problems in Computer Science. Among the different strategies propose to deal efficiently and effectively for this purpose, we highlight those related to clustering, more specifically, density-based clustering strategies, which stands out for its ability to define clusters of arbitrary shape and the robustness to deal with the presence of data noise, such as DBSCAN and OPTICS. However, these algorithms are still a computational challenge since they are distance-based proposals. In this work we present a new approach to make OPTICS feasible based on data indexing strategy. Although the simplicity with which the data are indexed, using graphs, it allows explore various parallelization opportunities, which were explored using graphic processing unit (GPU). Based on this structure, the complexity of OPTICS is reduced to O(E*logV) in the worst case, becoming itself very fast. In our evaluation we show that our proposal can be over 200x faster than its sequential version using CPU.