相关论文: Adaptive isogeometric analysis with hierarchical b…

This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivial topologies. Nonetheless, especially for hexahedral meshes,…

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been…

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…

Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type basis functions, that are able to hold a global smoothness…

We present a framework for solving the triharmonic equation over bilinearly parameterized planar multi-patch domains by means of isogeometric analysis. Our approach is based on the construction of a globally $C^2$-smooth isogeometric spline…

Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are…

In this work we address the complexity problem of the isogeometric Boundary Element Method by proposing a collocation scheme for practical problems in linear elasticity and the application of hierarchical matrices. For mixed boundary value…

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…

The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…

In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and…

We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…

We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…

We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…

We study approximation error bounds of isogeometric function spaces on a specific type of singularly parameterized domains. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a…

We present a completeness characterization of box splines on three-directional triangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties. For any given Type-I box spline, of specific maximum degree…

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…

One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…

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)…