相关论文: BPX Preconditioners for Isogeometric Analysis Usin…

This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…

We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…

We introduce a low-rank framework for adaptive isogeometric analysis with truncated hierarchical B-splines (THB-splines) that targets the main bottleneck of local refinement: memory- and time-intensive matrix assembly once the global…

For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal mesh-size. Therefore, reliable and effective numerical computations, in particular on…

Folding grid value vectors of size $2^L$ into $L$th order tensors of mode sizes $2\times \cdots\times 2$, combined with low-rank representation in the tensor train format, has been shown to lead to highly efficient approximations for…

Tensor B-spline methods are a high-performance alternative to solve partial differential equations (PDEs). This paper gives an overview on the principles of Tensor B-spline methodology, shows their use and analyzes their performance in…

Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…

We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at…

Preconditioning for multilevel Toeplitz systems has long been a focal point of research in numerical linear algebra. In this work, we develop a novel preconditioning method for a class of nonsymmetric multilevel Toeplitz systems, which…

Local refinement is vital for efficient numerical simulations. In the context of Isogeometric Analysis (IGA), hierarchical B-splines have gained prominence. The work applies the methodology of truncated hierarchical B-splines (THB-splines)…

The multilevel Schwarz preconditioner is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its parallel implementation on arbitrary unstructured triangular/tetrahedral…

Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…

A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient…

We describe our software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available as a stand-alone serial library, as an external package to PETSc (``Portable, Extensible…

This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The proposed strategy enhances locally-refined meshes for specific applications, simplifying…

In this paper we propose a local projector for truncated hierarchical B-splines (THB-splines). The local THB-spline projector is an adaptation of the B\'ezier projector proposed by Thomas et al. (Comput Methods Appl Mech Eng 284, 2015) for…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline…

Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…

We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…