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

Algorithm 4

SpMV kernel for the SBELL format.

       spmv_sbell_kernel(int𝑁𝑏,int𝑆𝑏,int𝑇,int^∗MnzbPerRow, 𝑖𝑛𝑡^∗𝑛𝑛𝑧𝑏,

               int^∗𝐵𝐽𝐴,float^∗𝐵𝐴,float^∗𝑥,float^∗𝑦)

       {

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

       int 𝑠𝑖𝑑=𝑡ℎ𝑟𝑒𝑎𝑑_𝑖𝑑/𝑇;

       int 𝑡𝑖𝑑=𝑡ℎ𝑟𝑒𝑎𝑑_𝑖𝑑−𝑠𝑖𝑑∗𝑇;

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

       int 𝑛𝑠𝑙𝑖𝑐𝑒=(𝑁𝑏+𝑆𝑏−1)/𝑆𝑏;

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

     for (𝑖𝑏=𝑡𝑖𝑑;𝑖<𝑆𝑏;𝑖𝑏+=𝑇){

    int 𝑏𝑟𝑜𝑤=𝑖𝑠×𝑆𝑏+𝑖𝑏;

    if (𝑏𝑟𝑜𝑤<𝑁𝑏){

            for (int𝑘𝑏=0;𝑘𝑏<  MnzbPerRow[is]; 𝑘𝑏++){

      int 𝑏𝑐𝑜𝑙=𝐵𝐽𝐴[𝑛𝑛𝑧[𝑖𝑠]+𝑆𝑏×𝑘𝑏+𝑖𝑏];

            for (𝑖=0;𝑖<𝑏𝑠𝑖𝑧𝑒;𝑖++)

          for (𝑗=0;𝑗<𝑏𝑠𝑖𝑧𝑒;𝑗++)

         int 𝑐𝑜𝑙=𝑏𝑠𝑖𝑧𝑒∗𝑏𝑐𝑜𝑙+𝑗;

            𝑘=𝑖∗𝑏𝑠𝑖𝑧𝑒+𝑗;

          𝑦[𝑏𝑟𝑜𝑤∗𝑏𝑠𝑖𝑧𝑒+𝑖]+=𝐵𝐴[𝑛𝑛𝑧𝑏[𝑖𝑠]∗𝑏𝑠𝑖𝑧𝑒∗𝑏𝑠𝑧𝑖𝑒+𝑗𝑏∗𝑆∗𝑏𝑠𝑧𝑖𝑒∗𝑏𝑠𝑖𝑧𝑒

                   +𝑘∗𝑏𝑠𝑖𝑧𝑒+𝑏𝑟𝑜𝑤]×𝑥[𝑐𝑜𝑙];}

             }

            }

           }

  }

  }

    }