Lectures:
Systems of equations arising from mathematical modelling in engineering.
Properties of systems arising from finite element methods.
Classical iterative methods. Richardson, Jacobi, Gauss-Seidel iterative methods. Convergence studies.
Multigrid methods.
Method of conjugate gradients. Fundamentals. Implementation.
Global properties and convergence rate estimates based on the condition number.
Preconditioning. Preconditioned conjugate gradients method. Incomplete factorization.
Solution to nonsymmetric systems. GMRES.
Solution to nonlinear systems. Properties of nonlinear operators. Newton method. Local convergence. Inexact Newton method. Damping and global convergence.
Implementation of iterative methods on parallel computers. Domain decomposition methods.
Comparison of direct and iterative methods. Solution to large-scale systems.
Tutorials:
Systems of equations arising in mathematical modeling in engineering. Assembling the system matrix in the finite element method, properties.
Solution to systems using Richardson, Jacobi, and Gauss-Seidel iterative methods. Multigrid method.
Implementation of conjugate gradient method, rate of convergence.
Implementation of various preconditioners in the conjugate gradients method. Incomplete factorization.
Implementation of GMRES.
Implementation of Newton method and inexact Newton method.
Implementation of iterative methods on parallel computers. Domain decomposition methods.
Comparison of direct and iterative methods. Solution to large-scale systems.
Systems of equations arising from mathematical modelling in engineering.
Properties of systems arising from finite element methods.
Classical iterative methods. Richardson, Jacobi, Gauss-Seidel iterative methods. Convergence studies.
Multigrid methods.
Method of conjugate gradients. Fundamentals. Implementation.
Global properties and convergence rate estimates based on the condition number.
Preconditioning. Preconditioned conjugate gradients method. Incomplete factorization.
Solution to nonsymmetric systems. GMRES.
Solution to nonlinear systems. Properties of nonlinear operators. Newton method. Local convergence. Inexact Newton method. Damping and global convergence.
Implementation of iterative methods on parallel computers. Domain decomposition methods.
Comparison of direct and iterative methods. Solution to large-scale systems.
Tutorials:
Systems of equations arising in mathematical modeling in engineering. Assembling the system matrix in the finite element method, properties.
Solution to systems using Richardson, Jacobi, and Gauss-Seidel iterative methods. Multigrid method.
Implementation of conjugate gradient method, rate of convergence.
Implementation of various preconditioners in the conjugate gradients method. Incomplete factorization.
Implementation of GMRES.
Implementation of Newton method and inexact Newton method.
Implementation of iterative methods on parallel computers. Domain decomposition methods.
Comparison of direct and iterative methods. Solution to large-scale systems.