Acceleration of boundary element calculations for closed domain using nonlinear form functions and CUDA technology

Abstract

The evolution of computer technologies, as a hardware and a software parts, allows to attain fast and accurate  solutions  to  many  applied  problems  in  scientific  areas.  Acceleration  of  calculations  is  broadly  used technic that is basically implemented by multithreading and multicore processors. NVidia CUDA technology or simply CUDA opens a way to efficient acceleration of boundary elements method (BEM), that includes many independent stages. The main goal of the paper is implementation and acceleration of indirect boundary element method using three form functions. Calculation of the potentialdistribution inside a closed boundary under the action of the defined boundary condition is considered. In order to accelerate corresponding calculations, they were parallelized at the graphic accelerator using NVidia CUDA technology. The dependences of acceleration of parallel  computations  as  compared  with  sequential  ones  were explored  for  different  numbers  of  boundary elements  and  computational  nodes.  A  significant  acceleration  (up  to  52  times)  calculation  of  the  potential distribution  without  loss  in  accuracy  is  shown.  Acceleration  of up  to  22  times  was  achieved  in  calculation of mutual  influence  matrix  for  boundary  elements.  Using  CUDA  technology  allows  to  attain  significant acceleration without loss in accuracy and convergence. So application of CUDA is a good way to parallelizing BEM.  Application  of  developed  approach  allows  to  solve  problems in  different  areas  of  physics  such as acoustics, hydromechanics, electrodynamics, mechanics of solids and many other areas, efficiently.