Solving large sparse eigenvalue problems on supercomputers

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed

A methodology for exploiting parallelism in the finite element process

A methodology is described for developing a parallel system using a top down approach taking into account the requirements of the user. Substructuring, a popular technique in structural analysis, is used to illustrate this approach

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

A distributed and iterative method for square root filtering in space-time estimation

Caption title.Includes bibliographical references.Supported by the Air Force Office of Scientific Research. F49620-92-J-002 Supported by the Office of Naval Research. N00014-91-J-1120 N00014-91-J-1004 Supported by the Army Research Office. DAAL03-92-G-0115Toshio M. Chin, William C. Karl, Alan S. Willsky

Time-power-energy balance of BLAS kernels in modern FPGAs

Conference proceedings 2022High Performance Computing. 9th Latin American Conference, CARLA 2022, Porto Alegre, Brazil, 26-30 sep 2022, Revised Selected Papers.Numerical Linear Algebra (NLA) is a research field that in the last decades has been characterized by the use of kernel libraries that are de facto standards. One of the most remarkable examples, in particular in the HPC field, is the Basic Linear Algebra Subroutines (BLAS). Most BLAS operations are fundamental in multiple scientific algorithms because they generally constitute the most computationally expensive stage. For this reason, numerous efforts have been made to optimize such operations on various hardware platforms. There is a growing concern in the high-performance computing world about power consumption, making energy efficiency an extremely important quality when evaluating hardware platforms. Due to their greater energy efficiency, Field-Programmable Gate Arrays (FPGAs) are available today as an interesting alternative to other hardware platforms for the acceleration of this type of operation. Our study focuses on the evaluation of FPGAs to address dense NLA operations. Specifically, in this work we explore and evaluate the available options for two of the most representative kernels of BLAS, i.e. GEMV and GEMM. The experimental evaluation is carried out in an Alveo U50 accelerator card from Xilinx and an Intel Xeon Silver multicore CPU. Our findings show that even in kernels where the CPU reaches better runtimes, the FPGA counterpart is more energy efficient.Los investigadores contaron con el apoyo de la Universidad de la República y el PEDECIBA.Se agradece a la ANII – MPG Independent Research Groups : “Efficient Hetergenous Computing” - CSC grou

Temporal unpredictability detection of real-time video sequence

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