Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems

Algorithm 3

SpMV kernel for the SELL format.

spmv_sell_kernel(int𝑁,int𝑆,int𝑇,int^∗MnzPerRow, int^∗𝑛𝑛𝑧,

          int ^∗𝐽𝐴,float^∗𝐴,float^∗𝑥,float^∗𝑦)

{

 int 𝑡ℎ𝑟𝑒𝑎𝑑_𝑖𝑑=𝑏𝑙𝑜𝑐𝑘𝐷𝑖𝑚.𝑥∗𝑏𝑙𝑜𝑐𝑘𝐼𝑑𝑥.𝑥+𝑡ℎ𝑟𝑒𝑎𝑑𝐼𝑑𝑥.𝑥;

 int 𝑠𝑖𝑑=𝑡ℎ𝑟𝑒𝑎𝑑_𝑖𝑑/𝑇;

 int𝑡𝑖𝑑=𝑡ℎ𝑟𝑒𝑎𝑑_𝑖𝑑-𝑠𝑖𝑑^∗𝑇;

 int 𝑛𝑢𝑚_𝑠𝑒𝑡𝑠=(𝑏𝑙𝑜𝑐𝑘𝐷𝑖𝑚.𝑥∗𝑔𝑟𝑖𝑑𝐷𝑖𝑚.𝑥)/𝑇;

 int 𝑛𝑠𝑙𝑖𝑐𝑒=(𝑁+𝑆−1)/𝑆;

 for (int𝑖𝑠=𝑠𝑖𝑑;𝑖𝑠<𝑛𝑠𝑙𝑖𝑐𝑒;𝑖𝑠+=𝑛𝑢𝑚_𝑠𝑒𝑡𝑠){

  for (𝑖=𝑡𝑖𝑑;𝑖<𝑆;𝑖+=𝑇){

   int 𝑟𝑜𝑤=𝑖𝑠×𝑆+𝑖;

   if (𝑟𝑜𝑤<𝑁){

    for (𝑘=0;𝑘< MnzPerRow[is];  𝑘 ++){

         int 𝑐𝑜𝑙=𝐽𝐴[𝑛𝑛𝑧[𝑖𝑠]+𝑆×𝑘+𝑖];

              𝑦[𝑖]+=𝐴[𝑛𝑛𝑧[𝑖𝑠]+𝑆×𝑘+𝑖]×𝑥[𝑐𝑜𝑙];}

   }

  }

   }

}