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Parallel Method for solving a Coupled PDE

Parallel Method for solving a Coupled PDE and its application in simulation of thin composite films. By: E. Nedaaee IASBS. What is thin film. Our Model:. , the order parameter which represents the difference between the densities of the two types of particles of the surface

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Parallel Method for solving a Coupled PDE

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  1. Parallel Method for solving a Coupled PDE and its application in simulation of thin composite films By: E. Nedaaee IASBS

  2. What is thin film

  3. Our Model: , the order parameter which represents the difference between the densities of the two types of particles of the surface , the height of the surface is thermal fluctuations of the flux of the incoming particles, such that represents the fluctuations in the density of the incoming particles with

  4. Discretization Fully implicit finite difference method

  5. Solve Nonlinear Set of Equations. Finish Algorithm Start Initial Conditions Yes No

  6. Nonlinear Solver Newton-Raphson Method

  7. Initial guess for X Return Solve. Set. Solving this linear set of equations by Conjugate-Gradient method and store J with sparse manner Yes No

  8. Parallelization Method Domain Decomposition Solve Nonlinear Set of Equations. In each domain Solve Nonlinear Set of Equations. In each domain z B.C. Exchange Finish Yes No Yes No

  9. MPI_Init(&argc, &argv); MPI_Comm_size(MPI_COMM_WORLD, &nump); MPI_Comm_rank(MPI_COMM_WORLD, &myrank); nump_row = (int) sqrt(nump); dims[0] = nump_row; dims[1] = nump_row; periods[0] = periods[1] = 1; MPI_Cart_create(MPI_COMM_WORLD, 2, dims, periods, 0, &comm); MPI_Comm_rank(comm, &myrank); MPI_Cart_coords(comm, myrank, 2, coords); MPI_Type_hvector(np,1,(np+2)*sizeof(double), MPI_DOUBLE, &BC); MPI_Type_commit(&BC);

  10. rcoords[0] = coords[0]; rcoords[1] = coords[1]+1; if(coords[1] == (nump_row-1)) rcoords[1] = 0; lcoords[0] = coords[0]; lcoords[1] = coords[1]-1; if(coords[1] == 0) lcoords[1] = nump_row - 1; bcoords[1] = coords[1]; bcoords[0] = coords[0]+1; if(coords[0] == (nump_row-1)) bcoords[0] = 0; tcoords[1] = coords[1]; tcoords[0] = coords[0]-1; if(coords[0] == 0) tcoords[0] = nump_row - 1; MPI_Cart_rank(comm, lcoords, &left); MPI_Cart_rank(comm, rcoords, &right); MPI_Cart_rank(comm, tcoords, &top); MPI_Cart_rank(comm, bcoords, &buttom);

  11. MPI_File_open(comm, fh_m_out,MPI_MODE_CREATE | MPI_MODE_RDWR, MPI_INFO_NULL, &fh_m); MPI_File_open(comm, fh_h_out,MPI_MODE_CREATE | MPI_MODE_RDWR, MPI_INFO_NULL, &fh_h); MPI_Barrier(comm); lsizes[0] = np; lsizes[1] = np; gsizes[0] = np*nump_row*file_size; gsizes[1] = np*nump_row; memsizes[0] = lsizes[0] + 2; memsizes[1] = lsizes[1] + 2; start_indices[0] = start_indices[1] = 1; MPI_Type_create_subarray(2,memsizes, lsizes, start_indices, MPI_ORDER_C,MPI_DOUBLE, &memtype); MPI_Type_commit(&memtype);

  12. start_indices[0] = coords[0]*lsizes[0]+count_ind*np*nump_row; start_indices[1] = coords[1]*lsizes[1]; MPI_Type_create_subarray(2,gsizes,lsizes,start_indices,MPI_ORDER_C,MPI_DOUBLE,&filetype); MPI_Type_commit(&filetype); MPI_File_set_view(fh_m, 0, MPI_DOUBLE, filetype, "native", MPI_INFO_NULL); MPI_File_set_view(fh_h, 0, MPI_DOUBLE, filetype, "native", MPI_INFO_NULL); MPI_File_write_all(fh_m,u_m, 1, memtype, &status); MPI_Wait(&req, &status); MPI_File_write_all(fh_h,u_h, 1, memtype, &status); MPI_Wait(&req, &status); MPI_Barrier(comm); count_ind +=1;

  13. for(;;){ vecfunc(x); newt(x, &check,vecfunc); MPI_Barrier(comm); BC_exchange(left,right,top,buttom); MPI_Barrier(comm); pnorm_s = NORM(x,x_temp); MPI_Allreduce(&pnorm_s, &pnorm_r, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); if(sqrt(pnorm_r) <= 1.e-9) break; for(int i = 1; i<= 2*np*np; i++) x_temp[i] = x[i]; count +=1;}

  14. void BC_exchange(int left, int right, int top, int buttom){ /*send and received from left neighbor*/ MPI_Isend(&u_h[1][1],np,MPI_DOUBLE, top,0,MPI_COMM_WORLD, &requests[0]); MPI_Irecv(&u_h[0][1],np,MPI_DOUBLE, top,0,MPI_COMM_WORLD, &requests[1]); /*send and received from right neighbor*/ MPI_Isend(&u_h[np][1],np,MPI_DOUBLE, buttom,0,MPI_COMM_WORLD, &requests[2]); MPI_Irecv(&u_h[np+1][1],np,MPI_DOUBLE,buttom,0,MPI_COMM_WORLD, &requests[3]); /*send and received from top neighbor*/ MPI_Isend(&u_h[1][np],1,BC, right,0,MPI_COMM_WORLD, &requests[4]); MPI_Irecv(&u_h[1][np+1],1,BC,right,0,MPI_COMM_WORLD, &requests[5]); /*send and received from bottom neighbor*/ MPI_Isend(&u_h[1][1],1,BC, left,0,MPI_COMM_WORLD, &requests[6]); MPI_Irecv(&u_h[1][0],1,BC, left,0,MPI_COMM_WORLD, &requests[7]); MPI_Waitall(8,requests, statuses);

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