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Highlights • We derive the model of concurrency for refined isogeometric analysis. • We associate basic undividable tasks with macro-elements separated by C0 hyperplanes. • We define the communication channels between tasks. • We aggregate the tasks to map into architecture of distributed memory parallel machine. • We analyse the computational and communicational costs of the resulting algorithm. Abstract We perform the analysis of the concurrency of the parallel refined isogeometric analysis (rIGA) computations. Namely, we consider three-dimensional mesh partitioned into several macro-elements, with tensor product B-spline basis functions, and C° separators introduced between the macro-elements. We partition the computational problem into a sequence of tasks, and we define the dependency relation between the tasks. Next, we use the trace theory approach to identify the sets of tasks that can be executed in concurrent, one set after the other. We also estimate the computational cost of the tasks. To generalize our model for the distributed memory case, we use the Partitioning Communication Agglomeration and Mapping (PCAM) model with tasks and communication channels mapped into the architecture of the parallel distributed memory machine. We perform numerical experiments on the representative three-dimensional meshes partitioned into macro-elements with quadratic and cubic B-splines, and we compare the numerical results with theoretical estimates. [ABSTRACT FROM AUTHOR]

This paper develops a coupling approach which integrates the meshfree method and isogeometric analysis (IGA) for static and free-vibration analyses of cracks in thin-shell structures. In this approach, the domain surrounding the cracks is represented by the meshfree method while the rest domain is meshed by IGA. The present approach is capable of preserving geometry exactness and high continuity of IGA. The local refinement is achieved by adding the nodes along the background cells in the meshfree domain. Moreover, the equivalent domain integral technique for three-dimensional problems is derived from the additional Kirchhoff-Love theory to compute the J-integral for the thin-shell model. The proposed approach is able to address the problems involving through-the-thickness cracks without using additional rotational degrees of freedom, which facilitates the enrichment strategy for crack tips. The crack tip enrichment effects and the stress distribution and displacements around the crack tips are investigated. Free vibrations of cracks in thin shells are also analyzed. Numerical examples are presented to demonstrate the accuracy and computational efficiency of the coupling approach. [ABSTRACT FROM AUTHOR]

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles. [ABSTRACT FROM AUTHOR]

Isogeometric analysis is a method for solving geometric partial differential equations (PDEs). Generating parametrizations of a PDE’s physical domain is a basic and important issue within isogeometric analysis framework. In this paper, we present a global H 1 -parametrization method for a complex planar physical domain. [ABSTRACT FROM AUTHOR]

The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline spaces but of a different degree. In one case, we consider an equal order pairing for which a cross point modification based on a local degree reduction is required. In the other case, the degree of the dual space is reduced by two compared to the primal. This pairing is proven to be inf–sup stable without any necessary cross point modification. Several numerical examples confirm the theoretical results and illustrate additional aspects. [ABSTRACT FROM AUTHOR]