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We introduce a novel quadrature strategy for Isogeometric Analysis (IgA) boundary element discretizations, specifically tailored to collocation methods. Thanks to the dimensionality reduction and the natural handling of unbounded domains,…
The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators…
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…
Solving arithmetic tasks is a simple and fundamental skill, yet modern Large Language Models (LLMs) have great difficulty with them. We introduce the Integrated Gated Calculator (IGC), a module that enables LLMs to perform arithmetic by…
Recent advancements in finite element methods allows for the implementation of mesh cells with curved edges. In the present work, we develop the tools necessary to employ multiply connected mesh cells, i.e. cells with holes, in planar…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
Isogeometric analysis (IGA) has proven to be an improvement on the classical finite element method (FEM) in several fields, including structural mechanics and fluid dynamics. In this paper, the performance of IGA coupled with the infinite…
Building Information Modeling (BIM) technology is a key component of modern construction engineering and project management workflows. As-is BIM models that represent the spatial reality of a project site can offer crucial information to…
We extend the softFEM idea to isogeometric analysis (IGA) to reduce the stiffness (consequently, the condition numbers) of the IGA discretized problem. We refer to the resulting approximation technique as softIGA. We obtain the resulting…
We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric…
This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a new developed…
In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
Immersed finite element methods have been developed as a means to circumvent the costly mesh generation required in conventional finite element analysis. However, the numerical ill-conditioning of the resultant linear system of equations in…
Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…
Most large engineering structures are described as assemblies of plates and shells and they are computed as such using adhoc Finite Element packages. In fact their computation in 3D would be much too costly. In this framework, the…
The production of lightweight metal lattice structures has received much attention due to the recent developments in additive manufacturing (AM). The design flexibility comes, however, with the complexity of the underlying physics. In fact,…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
Computational Fluid Dynamics (CFD) is widely used in different engineering fields, but accurate simulations are dependent upon proper meshing of the simulation domain. While highly refined meshes may ensure precision, they come with high…