Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Reactive sputter magnetron reactor for preparation of thin films and simultaneous in-situ structural study by X-ray diffraction.

Reactive Sputter Magnetron (RSM) is a widely used technique to thin films growing of compounds both, in research laboratories and in industrial processes. The nature of the deposited compound will depend then on the nature of the magnetron target and the nature of the ions generated in the plasma. One important aspect of the problem is the knowledge of the evolution of the film during the process of growing itself. In this work, we present the design, construction of a chamber to be installed in the Huber goniometer in the XRD2 line of LNLS in Campinas, which allows in situ growing kinetic studies of thin films.

Solitons in nonlinear Schrödinger equations.

Using a mathematical approach accessible to graduate students of physics and engineering, we show how solitons are solutions of nonlinear Schrödinger equations. Are also given references about the history of solitons in general, their fundamental properties and how they have found applications in optics and fiber-optic communications.