Solving the Caputo Fractional Reaction-Diffusion Equation on GPU

Algorithm 1

Parallel solution for Caputo fractional reaction-diffusion equation with CUDA.

(1)    Init CUDA environment

(2)   Allocate GPU global memory 𝐴,𝑈,𝐹,𝑟,𝑏….

(3)   Init variables and arrays on GPU

(4)   record time 𝑇₁

(5)   call kernel 𝑖𝑛𝑖𝑡𝑈⁰⟨⟨⟨𝑀/BS,BS⟩⟩⟩(…)

(6)   for  𝑛=1  to  𝑁  by Step  1 do

(7)               call kernel 𝑡𝑟𝑖𝑚𝑣𝑚𝐶𝑈⟨⟨⟨𝑀/BS,BS⟩⟩⟩(…)

(8)               call kernel 𝑐𝑣𝑚_𝑣𝑣𝑎𝐶𝑈⟨⟨⟨𝑀/BS,BS⟩⟩⟩(…)

(9)               for  𝑘=1  to  𝑛  by Step  1 do

(10)                     call kernel 𝑐𝑣𝑚𝑎𝐶𝑈⟨⟨⟨𝑀/BS,BS⟩⟩⟩(…)

(11)              call kernel 𝑐𝑣𝑚𝐶𝑈⟨⟨⟨𝑀/BS,BS⟩⟩⟩(…)

(12) record time 𝑇₂

(13) output 𝑇₂−𝑇₁ and 𝑈^𝑁…

(14) free GPU memory and stop CUDA environment