相关论文: Subdivision based Isogeometric Analysis technique …

We present implicit displacement fields, a novel representation for detailed 3D geometry. Inspired by a classic surface deformation technique, displacement mapping, our method represents a complex surface as a smooth base surface plus a…

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…

Locking is a common effect in finite element and isogeometric analysis. In the case of plates, transverse shear locking is most prominent, for shells several other types of locking exist. A common cure are mixed methods that introduce…

Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…

Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation…

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…

We study the dimension and construct a basis for $C^1$-smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined on a B-spline domain, whose graph surface also has a B-spline…

Neural network models often face challenges when processing very small or very large numbers due to issues such as overflow, underflow, and unstable output variations. To mitigate these problems, we propose using embedding vectors for…

We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations…

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…

We study the spectral approximation properties of isogeometric analysis with local continuity reduction of the basis. Such continuity reduction results in a reduction in the interconnection between the degrees of freedom of the mesh, which…

\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating…

The analysis of scattering from complex objects using surface integral equations is a challenging problem. Its resolution has wide ranging applications- from crack propagation to diagnostic medicine. The two ingredients of any integral…

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…

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 paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…

Alfv\'en-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex application, we focus on a parameter-dependent curl-div…