Recommended textbooks

mathematics
1

I am looking for textbook recommendations.

I am struggling with understanding how to 1) find the best / necessary fundamental equations, 2) understanding how to convert those equations into a form fenics understands, and 3) combining fundamental equations (Maxwell’s) with fitted equations (Hogdkin-Huxley-Katz).

I am primarily interested in electrodynamics and its interaction with biology (ionic solutions and complex geometry with varying impedance). I have an electrical engineering background.

I definitely need more background on variational problems / the FEM method, and the tutorial recommends several textbooks which sound like good options. I’m trying to avoid the thermodynamics-focused resources, since I don’t believe that’s relevant to my models. I’d appreciate resources with detailed / complicated electrodynamics examples that go beyond Laplace.

Thanks!

2

  1. Tom Hughes’s book for an intro to FEM.

  2. a) The FEniCS book (although it’s very outdated now) to get an idea of how FEniCS deals with FEM problems.
    b) @dokken’s excellent dolfinx tutorials.

  3. a) Jin’s book is probably a good start for electromagnetism and FEM from an engineering perspective.
    b) Peter Monk’s book to see all the detail of why FEM electromagnetism is very much not trivial.

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3

I can recommend B.E. Abali’s Book Computational Reality which offers a hands on approach to all kinds of coupled problems from various areas of classical physics using FEniCS. A plethora of examples starting with fundamental equations and assumptions leading up to the included runnable FEniCS code make the concepts easy to grasp.

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