elfem1

How to implement co/sine using One-Dimensional Finite Element Solver in Emacs Lisp ?

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The aim is to learn more about Emacs Lisp, starting from a subject that I master enough to focus on the language.

Therefore, the constraints of the exercice are:

1. consider the arithmetic operations: +,-,*,/ on integer and float
2. consider the elementary operations on list:
   • (list 1 2 3) creates the list 1,2,3
   • (car lst) return the first element of the list
   • (cdr lst) returns the rest of the list See Emacs Lisp, sec. List.
3. consider recursive function

The reference solution

    sin x = imaginary part of e^ix

and

    e^ix = sum_n=0 (ix)^n / n!

So, we need:

• Complex number and their associated operations (add, mul)
• Power
• Factorial

The overkilled solution

Let solve the differential equation:

    u'' + k^2 u = 0 in [0,1] with u(0)=1 and u'(1)=ik u(1)

by a finite element method.

So, we need:

• Matrix
• Inner product
• Matrix/Vector product
• Linear solver (e.g., Gauss pivot)

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Install / Run

    emacs -Q -batch -L . -l makefile.el -e do/all

• -Q avoids conflict with user configuration
• -batch means not interactive
• -L . prepends . to load-path; eases the (require stuff)
• -l makefile.el loads "nice" UI functions
• -e do/all launches the do/all functions (do/compile, do/test) note that do/clean removes all the .elc files