Reference book

Numerical Analysis

  • Richard L. Burden and J. Douglas Faires. Numerical analysis.

    • Numerical PDE and SDE

  • Hans Petter Langtangen, Svein Linge. Finite difference computing with PDEs, using Python.
  • Peter E. Kloeden and Eckhard Platen. Numerical solution of stochastic differential equations.
  • Bernt Oksendal. Stochastic differential equations: An introduction with applications.
  • Thomas Wick. Numerical Methods for Partial Differential Equations.

    • Micromagnetics

  • Boling Guo and Shijin Ding. Landau-Lifshitz equations.

    • Homogenization and Multiscale Methods

  • G.A. Pavliotis and A.M. Stuart. Multiscale methods: Averaging and homogenization.
  • Yalchin Efendiev and Thomas Y. Hou. Multiscale finite element methods: Theory and applications.
  • Weinan E. Principles of multiscale modeling.
  • Bj\"orn Engquist. Encyclopedia of Applied and Computational Mathematics.
  • Doina Cioranescu and Patrizia Donato. An introduction to homogenization.

    • Molecular simulation

  • Daan Frenkel and Berend Smit. Understanding molecular simulation: From algorithm and applications.

    • Electrodynamics

  • Fulvio Melia. Electrodynamics (Chicago Lectures in Physics).
  • Schwartz, Melvin. Principles of Electrodynamics.

    • Electronic structure calculations

  • Richard M. Martin. Electronic Structure: Basic Theory and Practical Methods.
  • Lin Lin and Jianfeng Lu. A Mathematical Introduction to Electronic Structure Theory.

    • Free boundary and Interface problems

  • Eberhard B\"ansch, Klaus Deckelnick, Harald Garcke and Paola Pozzi. Interfaces: Modeling, Analysis, Numerics (2023).
  • Edward Yu. Bormashenko. Wetting of real surfaces.
  • Kathrin Schulte, Cameron Tropea, Bernhard Weigand. Droplet dynamics under extreme ambient conditions.

    • Quantum computing and simulations

  • Daniel V. Schroeder. Notes on Quantum Mechanics (2022).

    • Fluid Structure Interaction and its applications

  • Yuri Bazilevs, Kenji Takizawa. Advances in computational FSI and flow simulation.
  • Georges-Henri Cottet, Emmanuel Maitre, Thomas Milcent. Level set methods for FSI.
  • Thomas Wick. Modeling, Discretization, Optimization, and Simulation of FSI.

    • Machine Learning for scientific computing

    Computational Fluid Mechanics

  • H. Yamaguchi. Engineering Fluid Mechanics.
  • Dongqing Li. Encyclopedia of Microfluidics and Nanofluidics.

    • Computational Solid Mechanics

    Mathematical modeling

  • Sam Howison. Practical Applied Mathematics: Modelling, Analysis, Approximation.

    • Numerical software for Simulations