Books and other learning material

In this page, you will find a list of essential reading material that is relevant to the kind of work I do. In each section, the books are roughly arranged in the order of increasing complexity.

Fluid Dynamics

  1. D. J. Tritton, Physical Fluid Dynamics
  2. John D. Anderson Jr., Modern compressible flow: With historical perspective.
  3. L. D. Landau and E. M. Lifschitz, Fluid Mechanics
  4. G. K. Batchelor, An Introduction to Fluid Dynamics

Partial Differential Equations

  1. Karl E. Gustafson, Introduction to PDE and Hilbert Space Methods
  2. Heinz-Otto Kreiss and Jens Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations.
  3. L. C. Evans, Partial Differential Equations

Numerical methods for PDE

  1. Thomee and Larsson, Partial Differential Equations with Numerical Methods
  2. Randall J. LeVeque, Numerical Methods for Conservation Laws.
  3. Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems.
  4. E. Godlewski and P. Raviart, Hyperbolic Systems of Conservation Laws.
  5. E. Godlewski and P. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws.

Computational Fluid Dynamics

  1. John D. Anderson Jr., Computational Fluid Dynamics: The basics with applications
  2. E. F. Toro, Riemann solvers and numerical methods for fluid dynamics.
  3. Charles Hirsch, Numerical Computation of Internal and External Flows, Vol. I & II.

Finite Element Methods

  1. Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method.
  2. Dietrich Braess, Finite elements: Theory, fast solvers and applications in solid mechanics.
  3. Alfio Quarteroni and Alberto Valli, Numerical Approximation of Partial Differential Equations
  4. Philippe Ciarlet, The Finite Element Method for Elliptic Problems.

Numerical Linear Algebra, MPI, HPC

  1. Yousef Saad, Iterative Methods for Sparse Linear Systems
  2. Victor Eijkhout, Introduction to High Performance Scientific Computing (Download)
  3. Victor Eijkhout, Parallel Programming in Science and Engineering (Download)

Video lectures

  1. Gilbert Strang: Computational Science and Engineering I
  2. Gilbert Strang: Mathematical Methods for Engineers II
  3. Lorena Barba: Computational Fluid Dynamics
  4. Krishna Garikipati: Introduction to Finite Element Methods
  5. Wolfgang Bangerth: Finite element methods in scientific computing (based on deal.II)