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Scientific Computing Lab

Scientific Computing in Computer Science. Institut für Informatik. Scientific Computing Lab. Results Worksheet 3. Dr. Miriam Mehl. Worksheet 3 – Solution. N x = N y =3. Worksheet 3 – Solution. 1) m-file create_matrix.m for m=1:N_y for k=1:N_x i = (m-1)*N_x+k;

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Scientific Computing Lab

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  1. Scientific Computing in Computer Science Institut für Informatik Scientific Computing Lab Results Worksheet 3 Dr. Miriam Mehl

  2. Worksheet 3 – Solution Nx= Ny=3

  3. Worksheet 3 – Solution 1) m-file create_matrix.m for m=1:N_y for k=1:N_x i = (m-1)*N_x+k; A(i,i) = -2*(N_x+1)^2-2*(N_y+1)^2; if ~(k==1) A(i,i-1) = (N_x+1)^2; end … if ~(m==1) A(i,i-N_x) = (N_y+1)^2; end … end end

  4. Worksheet 3 – Solution 2) m-file GaussSeidel.m while (res>0.0001) res=0.0; for m=2:N_y+1 for k=2:N_x+1 x_m(k,m)=(d_1*(x_m(k-1,m)+x_m(k+1,m))+… end end for m=2:N_y+1 for k=2:N_x+1 res=res+(b((m-2)*N_x+k-1)+a_ii*x_m(k,m)-… end end res=sqrt(res/(N_x*N_y)); end

  5. Worksheet 3 – Solution 3) m-file worksheet3.m tic; x=A\b; time(1)=toc; memory(1)=numel(A)+numel(b)+numel(x); %transform x to a matrix for visualisation x_m=zeros(N_x+2,N_y+2); for k=2:N_x+1 for m=2:N_y+1 x_m(k,m)=x((m-2)*N_x+k-1); end end … subplot(2,1,1); mesh(coord1,coord2,x_m); subplot(2,1,2);contour(coord1,coord2,x_m);

  6. Worksheet 3 – Solution 3) m-file worksheet3.m S=sparse(A); tic; x=S\b; time(2)=toc; memory(2)=nnz(S)+numel(b)+numel(x);

  7. Worksheet 3 – Solution 3) m-file worksheet3.m tic; x_m=GaussSeidel(b,N_x,N_y); time(3)=toc memory(3)=numel(b)+numel(x_m)

  8. Worksheet 3 – Solution Nx= Ny=7

  9. Worksheet 3 – Solution Nx= Ny=15

  10. Worksheet 3 – Solution Nx= Ny=31

  11. Worksheet 3 – Solution Nx= Ny=63

  12. Worksheet 3 – Solution direct solution with full matrix

  13. Worksheet 3 – Solution direct solution with sparse matrix

  14. Worksheet 3 – Solution Gauss-Seidel without explicit matrix

  15. Worksheet 3 – Solution error – convergence order q=2

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