Nonlinearity: Methods and Examples

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Related lectures (30)

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Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Diffusion-Convection: Modeling and Schemes

Covers modeling and numerical schemes for diffusion-convection problems.

Solving the linear system - Nonlinearity

Explores solving linear systems and addressing nonlinearity in numerical flow simulations using multigrid and linearization methods.

Linear Systems: Iterative Methods

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Numerical Analysis: Linear Systems

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Computation, Verification and Validation

Explains verification and validation in CFD simulations, focusing on Richardson extrapolation and accuracy checking.

Fluid Dynamics: Differential Conservation Laws and Equations

Covers the differential approach to fluid dynamics, focusing on conservation laws and the Cauchy stress tensor.

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Heat Equation: Modeling and Numerical Methods

Covers the heat equation, its physical interpretation, and numerical methods for solving it.