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

Algorithm 1

Preconditioned conjugate gradient.

𝐫₀=𝐛−𝐀𝐱₀,𝐳₀=𝐌⁻¹𝐫₀,𝐩₀=𝐳₀

for 𝑗=0,1,…, until convergence

 𝛼_𝑗=(𝐫_𝑗,𝐳_𝑗)/(𝐀𝐩_𝑗,𝐩_𝑗)

 𝐱_𝑗+1=𝐱_𝑗+𝛼_𝑗𝐩_𝑗

 𝐫_𝑗+1=𝐫_𝑗−𝛼_𝑗𝐀𝐩_𝑗

 𝐳_𝑗+1=𝐌⁻¹𝐫_𝑗+1

 𝛽_𝑗=(𝐫_𝑗+1,𝐳_𝑗+1)/(𝐫_𝑗,𝐳_𝑗)

 𝐩_𝑗+1=𝐳_𝑗+1+𝛽_𝑗𝐩_𝑗

end for