scholarly journals On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe

2010 ◽  
Vol 32 (2) ◽  
pp. 656-683 ◽  
Author(s):  
Ümt V. Çatalyürek ◽  
Cevdet Aykanat ◽  
Bora Uçar
Keyword(s):  
Sparse Matrix ◽  
Two Dimensional ◽  
Matrix Partitioning

Two-Dimensional Approaches to Sparse Matrix Partitioning

2012 ◽  
pp. 321-349 ◽  
Author(s):  
Rob Bisseling ◽  
Bas Auer ◽  
A Yzelman ◽  
Tristan van Leeuwen ◽  
Ümit Çatalyürek
Keyword(s):  
Sparse Matrix ◽  
Two Dimensional ◽  
Matrix Partitioning

scholarly journals Sparse matrix partitioning for optimizing SpMV on CPU-GPU heterogeneous platforms

2019 ◽  
Vol 34 (1) ◽  
pp. 66-80 ◽  
Author(s):  
Akrem Benatia ◽  
Weixing Ji ◽  
Yizhuo Wang ◽  
Feng Shi
Keyword(s):  
Graphics Processing Units ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Heterogeneous Systems ◽  
Input Matrix ◽  
Heterogeneous Platforms ◽  
Mapping Algorithm ◽  
Matrix Vector Multiplication ◽  
Graphics Processing ◽  
Matrix Partitioning

Sparse matrix–vector multiplication (SpMV) kernel dominates the computing cost in numerous applications. Most of the existing studies dedicated to improving this kernel have been targeting just one type of processing units, mainly multicore CPUs or graphics processing units (GPUs), and have not explored the potential of the recent, rapidly emerging, CPU-GPU heterogeneous platforms. To take full advantage of these heterogeneous systems, the input sparse matrix has to be partitioned on different available processing units. The partitioning problem is more challenging with the existence of many sparse formats whose performances depend both on the sparsity of the input matrix and the used hardware. Thus, the best performance does not only depend on how to partition the input sparse matrix but also on which sparse format to use for each partition. To address this challenge, we propose in this article a new CPU-GPU heterogeneous method for computing the SpMV kernel that combines between different sparse formats to achieve better performance and better utilization of CPU-GPU heterogeneous platforms. The proposed solution horizontally partitions the input matrix into multiple block-rows and predicts their best sparse formats using machine learning-based performance models. A mapping algorithm is then used to assign the block-rows to the CPU and GPU(s) available in the system. Our experimental results using real-world large unstructured sparse matrices on two different machines show a noticeable performance improvement.

A finite‐element solution for the transient electromagnetic response of an arbitrary two‐dimensional resistivity distribution

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1450-1461 ◽  
Author(s):  
Y. Goldman ◽  
C. Hubans ◽  
S. Nicoletis ◽  
S. Spitz
Keyword(s):  
Finite Element ◽  
Sparse Matrix ◽  
Equation System ◽  
Electromagnetic Response ◽  
Implicit Time ◽  
Two Dimensional ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Exact Boundary ◽  
The Time Domain

We present a numerical method for solving Maxwell’s equations in the case of an arbitrary two‐dimensional resistivity distribution excited by an infinite current line. The electric field is computed directly in the time domain. The computations are carried out in the lower half‐space only because exact boundary conditions are used on the free surface. The algorithm follows the finite‐element approach, which leads (after space discretization) to an equation system with a sparse matrix. Time stepping is done with an implicit time scheme. At each time step, the solution of the equation system is provided by the fast system ICCG(0). The resulting algorithm produces good results even when large resistivity contrasts are involved. We present a test of the algorithm’s performance in the case of a homogeneous earth. With a reasonable grid, the relative error with respect to the analytical solution does not exceed 1 percent, even 2 s after the source is turned off.

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