Related papers: A sparse-grid isogeometric solver
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…
We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union and intersection. Particularly, this work focuses on the union…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of…
This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential…
A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale…
This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a…
Sparse grids are popular tools for high-dimensional function approximation. In this work, we study the use of sparse grids for interpolation using separable Mat\'ern kernels…
Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near corners limit the effectiveness of IGA, since standard methods…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
We propose the use of sparse grids to accelerate particle-in-cell (PIC) schemes. By using the so-called `combination technique' from the sparse grids literature, we are able to dramatically increase the size of the spatial cells in…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
Shell structures with a high stiffness-to-weight ratio are desirable in various engineering applications. In such scenarios, topology optimization serves as a popular and effective tool for shell structures design. Among the topology…
Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with…
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…
This work introduces and analyzes B-spline approximation spaces defined on general geometric domains obtained through a mapping from a parameter domain. These spaces are constructed as sparse-grid tensor products of univariate spaces in the…
This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA…