An isogeometric mortar method for the coupling of multiple NURBS domains with optimal convergence rates

We investigate the mortar finite element method for second order elliptic boundary value problems on domains which are decomposed into patches $$\Omega _k$$ Ω k with tensor-product NURBS parameterizations. We follow the methodology of IsoGeometric Analysis (IGA) and choose discrete spaces $$X_{h,k}$$ X h , k on each patch $$\Omega _k$$ Ω k as tensor-product NURBS spaces of the same or higher degree as given by the parameterization. Our work is an extension of Brivadis et al. (Comput Methods Appl Mech Eng 284:292–319, 2015) and highlights several aspects which did not receive full attention before. In particular, by choosing appropriate spaces of polynomial splines as Lagrange multipliers, we obtain a uniform infsup-inequality. Moreover, we provide a new additional condition on the discrete spaces $$X_{h,k}$$ X h , k which is required for obtaining optimal convergence rates of the mortar method. Our numerical examples demonstrate that the optimal rate is lost if this condition is neglected.

Numerical Solution to the Contact Interaction Problem of Nuclear Fuel Element Components Using the Mortar Method and the Domain Decomposition Method

The paper presents algorithms for solving axisymmetric contact interaction problems for several thermoelastic bodies using unmatched meshes. We employed the finite element method to obtain numerical solutions to problems of thermal conductivity and the theory of elasticity. We took contact interaction into account by applying the mortar method and the method of domain decomposition. The mortar method requires solving an ill-conditioned system of linear algebraic equations with a zero block at the main diagonal. To solve it numerically, we used a modified method of successive over-relaxation (MSSOR), which makes it possible to reduce solving the system of equations for all contacting bodies to sequentially solving systems of equations for each body separately. We showcase our algorithm results by solving an example problem simulating thermomechanical processes in a nuclear fuel element. We analyse the features of the stress-strain state in the structure and compare the results obtained using the mortar method and the domain decomposition method. The computational domain in the problem considered consisted of 10 nuclear fuel pellets and a cladding section. The analysis results showed that the quantitative stress-strain state properties in a system of bodies obtained by the two methods are quite close to each other. This confirms the fact that these algorithms may be correctly applied to solving similar problems

Acoustics on small scales

We present a modelling strategy based on the finite element method to describe flexible, piezoelectric structures surrounded by a compressible fluid, including viscosity. Non-conforming interfaces based on the Mortar method are used to couple the different physical domains. Finally, we present an application example of a piezoelectrically actuated MEMS structure to illustrate the modeling procedure and the impact of viscous effects.