A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system the mass matrix at each step. For applications in structural dynamics, solution is frequently approximated through so-called lumping, which consists replacing by some diagonal approximation. Mass lumping has been widely used engineering practice for decades already and sound mathematical theory supporting it finite element methods using classical Lagrange basis. However, more general basis functions still missing. Our paper partly addresses this shortcoming. Some special practically relevant properties lumped matrices are proved we discuss how these naturally extend to banded Kronecker product whose structure allows solve systems very efficiently. theoretical results applied isogeometric but not restricted them.