Problem 2 : Assume that we use a (n n n) 3D grid for a Poisson volume solver. We also use n n x n processors located on each grid node. Each processor has six routing port registers, RE, RS, RW, RN RU, RD for data routing to east, south, west, north, up and down processors, respectively. Otherwise, the processors have very simple internal architecture, so that it is cost-effective to use many of them Specifically, cach processor has 16 general registers, standard (unpipelined) arithmetic functional units and limited memory. Only one processor instruction can be executed per cycle and every instruction takes one computation cycle. Basic processor instructions and formats are: LOAD Register Memory MOVE Register Register ROUTE Register STORE MEMORY ADD Register Register Register SUB Register Register Register MULT Register Register Register DIV Register Register Register Load register vith men value V both general and routing registers only routing registers Register Simple loop iteration instructions are also eeded. We assume bidirectional point-to-point interconnects in the processor mesh. a) Express in familiar grid notation the main 3D Poisson equation Write a parallel program in pseudo-code to solve the Poisson equation assuming al 64 64 64 grid. b) How many cycles does it take to execute 1000 iterations of this program in the parallel 3D mesh? No convergence test is performed. c) What is the speedup and efficiency of the parallel processor mesh scheme in comparison to a single processor solution. Assume that we use the same processor types in both cases. d) Estimate the memory data requirements per processor (only for data) concerning the parallel scheme. as well as the singke processor solution. Extra Credit. Build a C/C++program which implements the 3D Poisson solver using a simple initial condition: node (0.0,0) set at 10 C. Your program should emulate the Poisson solver operating sequentially on a single processor. Provide an output listing first for 10 and then 100 iterations. Is there any converging trend of the values in the 3D grid? Problem 2 : Assume that we use a (n n n) 3D grid for a Poisson volume solver. We also use n n x n processors located on each grid node. Each processor has six routing port registers, RE, RS, RW, RN RU, RD for data routing to east, south, west, north, up and down processors, respectively. Otherwise, the processors have very simple internal architecture, so that it is cost-effective to use many of them Specifically, cach processor has 16 general registers, standard (unpipelined) arithmetic functional units and limited memory. Only one processor instruction can be executed per cycle and every instruction takes one computation cycle. Basic processor instructions and formats are: LOAD Register Memory MOVE Register Register ROUTE Register STORE MEMORY ADD Register Register Register SUB Register Register Register MULT Register Register Register DIV Register Register Register Load register vith men value V both general and routing registers only routing registers Register Simple loop iteration instructions are also eeded. We assume bidirectional point-to-point interconnects in the processor mesh. a) Express in familiar grid notation the main 3D Poisson equation Write a parallel program in pseudo-code to solve the Poisson equation assuming al 64 64 64 grid. b) How many cycles does it take to execute 1000 iterations of this program in the parallel 3D mesh? No convergence test is performed. c) What is the speedup and efficiency of the parallel processor mesh scheme in comparison to a single processor solution. Assume that we use the same processor types in both cases. d) Estimate the memory data requirements per processor (only for data) concerning the parallel scheme. as well as the singke processor solution. Extra Credit. Build a C/C++program which implements the 3D Poisson solver using a simple initial condition: node (0.0,0) set at 10 C. Your program should emulate the Poisson solver operating sequentially on a single processor. Provide an output listing first for 10 and then 100 iterations. Is there any converging trend of the values in the 3D grid
