I Specific Examples Example 1: Matrix-vector multiplication using collective communication Example 2: Matrix-matrix multiplication using collective communication Example 3 Solving Poisson's equation through the use of ghost cells Example 4: Matrix-vector multiplication using a client-server approach
Specific Examples • Example 1: – Matrix-vector multiplication using collective communication. • Example 2: – Matrix-matrix multiplication using collective communication. • Example 3: – Solving Poisson's equation through the use of ghost cells. • Example 4: – Matrix-vector multiplication using a client-server approach
Example 1: Matrix-vector Multiplication The figure below demonstrates schematicall how a matrix-vector multiplication a=B*C, can be decomposed into four independent computations involving a scalar multiplying a column vector This approach is different from that which is usually taught in a linear algebra course because this decomposition lends itself better to parallelIzation These computations are independent and do not require communication, something that usually reduces performance of parallel code
Example 1: Matrix-vector Multiplication • The figure below demonstrates schematically how a matrix-vector multiplication, A=B*C, can be decomposed into four independent computations involving a scalar multiplying a column vector. • This approach is different from that which is usually taught in a linear algebra course because this decomposition lends itself better to parallelization. • These computations are independent and do not require communication, something that usually reduces performance of parallel code
Example 1: Matrix-vector Multiplication(Columnwise Figure 13.5. Schematic of parallel decomposition for vector-matrix multiplication, A=B*C. The vector a is depicted in yellow. The matrix B and vector C are depicted in multiple colors representing the portions columns, and elements assigned to each processor, respectively
Example 1: Matrix-vector Multiplication (Columnwise) Figure 13.5. Schematic of parallel decomposition for vector-matrix multiplication, A=B*C. The vector A is depicted in yellow. The matrix B and vector C are depicted in multiple colors representing the portions, columns, and elements assigned to each processor, respectively