Optimization Research Of Fast Solver For The Grad-shafranov Equation

In the process of the iterative computation of plasma equilibrium reconstruction,it is needed to fast solve Grad-Shafranov(G-S)equation.In the plasma equilibrium reconstruction code used in EAST,we use 5 point stencil to fast solve the equation in 65 X 65 mesh based on discrete sine transform(DST)technique,but the computing speed can not meet the need of real control when we make the mesh size 129×129 or 257×257.In the essay,we try some improvement of the algorithm and usethe fouth order compact scheme to discrete the G-S equation,which we use DST method to fast solve to get the better acceleration ratio.This method is successfully used in P-EFIT code.In the essay,we first describe the acceleration multigrid method based on GPU under low mesh,In serial computing,multigrid method is better than DST method,but we have proved that we can not get high acceleration ratio after many experiments.We conclude that parallel multigrid method can not meet the need of real control.We highly describe how to construct a fourth-order compact scheme of G-S equation and how to fast solve that equation based on DST technique.It turns out that in 65 X 65 mesh,if the right side current distribution is known,the time needed to solve the G-S equation based on GPU is about 34 ?s.In addition,we propose the estimation method of the values of the remain points after doubling the mesh sizes.Now the G-S equation used in real control is under 2 dimension,while the G-S equation belongs to elliptic differential equations.In the essay,we try to apply the DST technique to the fast solution of the 3D elliptic differential equations in regulate region and we use CUD A for parallel computing.