# Advantages of using BEM for contact problem over FEM

Are there any advantages of using BEM (Boundary Element Method) for contact problem over FEM (Finite Element Method) apart from lesser computational cost?

• I am not so sure that the BEM will have lesser computational costs over the FEM. Having smaller matrices is not the only to take into account when talking about computational cost. Commented Jul 23, 2022 at 14:19
• @nicoguaro as per my understanding, for the same element size, the DOF solved for using FEM would be larger than using BEM, and discretizing the entire volume would be much more computationally expensive than just discretizing the boundary. Commented Jul 23, 2022 at 20:43
• Yes, but matrices tend to be dense and not symmetric. Commented Jul 24, 2022 at 1:27
• That's exactly the point: A smaller system that is dense may be much harder to solve than a larger system that is sparse. I don't think it is universally accepted that the BEM is cheaper. Commented Jul 25, 2022 at 16:10
• After some more reading, I found out that BEM results in an exact solution due to the analytical expression relating displacements to traction. This happens because it takes the fundamental solution as a weighting function and the math that follows. What I don't understand is why can't we do the same in FEM (assume fundamental solution as shape function)? Commented Jul 27, 2022 at 22:59