The objective of the research group in Computational mathematics at Umeå University is to conduct research on novel computational methods for the solution of partial differential equations and to promote its application in education, science and engineering. Our research is cross-disciplinary and located in the intersection between mathematics, computer science, physics and applications.
Our research is particularly geared towards developing adaptive finite element methods, developing efficient and robust methods for solving multiscale and multiphysics problems and finding efficient solutions to large-scale problems using various model-reduction techniques.
Applications are found, for instance, in the simulation of complex mechanical systems and in biomechanics. The group’s activity spans several projects that are run in close collaboration with industrial partners. Together with SKF, we are developing new model-reduction methods with improved local accuracy for the simulation of, for example, rolling bearings and gear wheels. Together with Surgical Science, we are developing finite element methods for the real-time simulation of the deformation of, for example, organs, membranes and threads for use in surgical simulators. Another project in the same field is performed in collaboration with Karolinska Institutet and KTH, where we are developing a model for simulating blood flow through a beating human heart. Together with FOI, we are also modelling dispersion in urban environments to predict the outcome of accidents involving toxic gases