Topics covered in this school include partial differential equations, times series, introduction to iterative solvers for linear systems, Conjugate Gradient (CG), preconditioned CG, Fourier and polynomial spectral methods, design of scalable algorithms for particle-based simulation methods for CFD like Lattice Boltzmann methods (LBM), Hybrid Monte Carlo (HMC), symplectic integrators with multiple time-scales relevant for biological systems.

 

Material

Ordinary Differential Equations and Time Integration Methods

Partial Differential Equations and Galerkin Methods

Splitting Methods for Ordinary and Partial Differential Equations

Time Series Methods for Data Analysis

Waveform Relaxation Methods for Coupled Systems

Hamiltonian Systems Modelling and Numerical Simulation

Iterative Methods for Linear and Nonlinear Systems

Finite Volume Methods and Particle-Based Methods for CFD