CSDMS 2.0: Moving Forward

A very basic introduction to numerical methods for scientific computing

Hari Rajaram

University of Colorado, Boulder, United States

[[CSDMS meeting abstract presentation::I will give a overview of the basic foundations of numerical methods for modeling earth systems described by ordinary and partial differential equations. I will discuss the underlying foundations of finite-difference, finite-volume and finite-element methods using diffusion/conduction equations as an example. I will discuss explicit and implicit methods for time-stepping, and stability analysis of time-integration schemes. All numerical methods for ODEs and PDEs in some form arrive at algebraic approximations, translating them into systems of algebraic equations. I will discuss basic algorithms for solving systems of algebraic equations, and how they are incorporated into various software packages, and also emphasize the importance of sparsity in matrix computations. I will include examples derived from practical problems in reactive transport and glacier dynamics to illustrate how basic concepts apply to real-world problems and make a difference when we want to develop efficient and accurate models.

PDFs of the numerical methods for scientific computing clinic
1) Newton Raphson Iteration for solving nonlinear equations pdf
2) Solution of Laplace pdf
3) Illustration using the 1D heat equation pdf

Numerical methods for scientific computing clinic example files:
* Matlab files: zip


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Of interest for:
  • Terrestrial Working Group
  • Coastal Working Group
  • Marine Working Group
  • Education and Knowledge Transfer (EKT) Working Group