Martin Lanser's research focuses on the development and parallel implementation of linear and nonlinear domain decomposition methods for the numerical solution of partial differential equations. He is especially interested in robust and efficient methods for application problems in solid mechanics, like deformations of multiphase steels or laser beam welding problems. Martin Lanser implements the efficient domain decomposition methods that can be used on modern parallel hardware in the PETSc-based package FE2TI.

Another focus of his research work is on the field of scientific machine learning, more precisely on the combination of machine learning (ML) and domain decomposition methods. On the one hand, ML is used to accelerate the classical numerical methods, and, on the other hand, domain decomposition methods are used to parallelize the training of ML models.