Introduction to Scientific Computing II Institut für Informatik Scientific Computing In Computer Science Introduction to Scientific Computing II Conjugate Gradient Method Dr. Miriam Mehl

Steepest Descent – Convergence Poisson with 5-point-stencil like Jacobi/GS

Steepest Descent – Convergence

Conjugate Gradients – Basic Idea solution of SLE minimization iterative one-dimensional minima no repeating search directions

Steepest Descent – Principle

Conjugate Gradients – Principle

CG – Algorithm

Steepest Descent – Example initial error after 1 iteration after 10 iterations

Conjugate Gradients – Example initial error after 1 iteration after 10 iterations

Conjugate Gradients – Example Error after 50 iterations (h=1/128)

Conjugate Gradients – Example h iterations sd iterations cg #unknowns 1/16 646 35 225 1/32 2,744 76 961 1/64 11,576 157 3,969 1/128 48,629 322 16,129

CG – Convergence Poisson with 5-point-stencil like SOR no parameter adjustment