TY - GEN A1 - Dornisch, Wolfgang A1 - Stöckler, Joachim T1 - An isogeometric mortar method with optimal convergence and reduced support T2 - 24th International Conference on Computer Methods in Mechanics (CMM) and the 42nd Solid Mechanics Conference (SolMech) N2 - The main feature of isogeometric analysis is the usage of a coherent geometry description for design and analysis. In most cases, Non-Uniform Rational B-splines (NURBS) are used within the frame of the finite element method, which combines the most common geometrical modeling concept with the most common analysis method in structural mechanics. NURBS are a versatile tool for geometric modeling, and in order to define complex geometric structures, a multitude of tensor-product NURBS patches is required. Typical software in Computer-Aided design can manage smoothness requirements across common interfaces of neighboring patches. For the finite element method, a different type of coupling across interfaces must be achieved. Due to the nature of tensor product NURBS, the simple concept of mutual refinement and subsequent coupling by shared degrees of freedom is prohibitively costly and, in some cases, even not possible. A multitude of coupling methods has been proposed over the last years. The most common concepts are known as mortar methods. In particular, the dual mortar method has been shown to yield very efficient computations. A recent paper by the authors has provided an isogeometric mortar method with mathematically proven optimal convergence of the stress errors over the entire domain. We use dual basis functions, which have support only on one interface and avoid interrelations between different interfaces. Models with a large number of intersecting interfaces can be handled. However, the basis functions have full support on the interfaces. In our current contribution, we propose the use of approximate dual basis functions with the advantage of having local support on the interfaces. These functions fulfill the duality only in an approximate way, but still guarantee the optimal degree for the convergence of the mortar method. Since the duality is not fulfilled, an additional lumping of the mortar matrix is introduced. The error of this lumping can be analyzed mathematically and is not significant in comparison to the global approximation error of the finite element method. The use of the approximate dual basis functions restores the local support of basis functions along the interface while the convergence properties remain intact. Numerical examples show the convergence behavior for simple and complex models. Y1 - 2022 UR - https://opus4.kobv.de/opus4-UBICO/frontdoor/index/index/docId/29288 UR - http://cmm-solmech.ippt.pan.pl/S01.html#ID_119 ER -