# What are the prerequisites and resources to self-learn the Boundary Element Method for Contact Mechanics problems?

1. What are the prerequisites to learning BEM?
2. In which order is it advisable to learn BEM and FEM - either one before the other, or does it not matter?
3. What are some good resources to self-learn BEM?

P.S. I am mainly interested in contact mechanics of surfaces. I am a mechanical engineer (senior) by trade, and I have basic undergrad-level math background (calculus, odes, pdes, linear algebra). No advanced numerical techniques/FEM courses taken so far.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Jul 7, 2022 at 13:54
• In particular your math and computational backgrounds would help Readers to make more cogent suggestions about the steps "to self-learn BEM". Boundary element methods are limited to linear PDEs that can be formulated as integral equations. There are lots of applications, but tailored advice is likely to be more easily digested.
– hardmath
Jul 7, 2022 at 22:20

As prerequisites, I would say that you need to understand some theoretical aspects of PDEs. The following pop up in my mind, separation of variables (eigenfunctions of operators and Sturm-Liouville theory won't hurt), Fourier series and Fourier transform, and self-adjoint operators. How much of these you will need depends on the applications and approach wanted. For first-order (and higher-order) elements you would need some interpolation and numerical integration knowledge.

Since there is a wider literature and more software available, I would suggest starting with the finite element method.

Regarding references, I have not found a book (or monograph) that I consider good enough as self-learning material. That being said, I have been using reference 2 as the book for the course on Boundary elements that we have in our university. This course is intended for last-year undergrad and first-year grad students, mainly from civil and mechanical engineering.

Finally, reference 2 is a monograph dedicated solely to the boundary element in contact mechanics.

## References

1. Katsikadelis, J. T. (2016). The boundary element method for engineers and scientists: theory and applications. Academic Press.

2. Man, K. W. (1994). Contact mechanics using boundary elements.