XIGA: An eXtended IsoGeometric analysis approach for multi-material problems

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 accurate solutions remain challenging. Immersed boundary techniques provide elegant solutions for such...

An optimally convergent smooth blended B-spline construction for semi-structured quadrilateral and hexahedral meshes

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, the construction of smooth and optimally convergent isogeometric analysis basis functions is still an...

Extension of B-spline Material Point Method for unstructured triangular grids using Powell–Sabin splines

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross...

Nonlinear system identification with regularized Tensor Network B-splines

This article introduces the Tensor Network B-spline (TNBS) model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of dimensionality of multivariate B-splines by representing the high-dimensional weight tensor as a low-rank...

A 4D tomographic ionospheric model to support PPP-RTK

Successful implementation of integer ambiguity resolution enabled precise point positioning (aka PPP-RTK) algorithms is inextricably linked to the ability of a user to perform near real-time positioning by quickly and reliably resolving the integer carrier-phase ambiguities. In the PPP-RTK technique, a major barrier to successful ambiguity...

A High Order Material Point Method

The classical material point method (MPM) developed in the 90s is known for drawbacks which affect the quality of results. The movement of material points from one element to another leads to non-physical oscillations known as ‘grid crossing errors’. Furthermore, the use of material points as integration points renders a numerical quadrature...

Shape Parameterization in Aircraft Design: A Novel Method, Based on B-Splines

This thesis introduces a new parameterization technique based on the Class-Shape-Transformation (CST) method. The new technique consists of an extension to the CST method in the form of a refinement function based on B-splines. This Class-Shape-Refinement-Transformation (CSRT) method has the same advantages as the original CST method, while also...