# Isogeometric Analysis on V-reps: first results

## TL;DR

This paper introduces a new isogeometric analysis method for solving elliptic PDEs on trimmed geometries represented as V-reps, with theoretical validation and practical testing in 2D and 3D.

## Contribution

It develops a novel approach for isogeometric analysis on V-reps, including approximation tools and re-parametrization techniques for trimmed geometries.

## Key findings

- Validated on 2D and 3D diffusion problems
- Successfully applied to linear elasticity problems
- Theoretical framework supports algorithmic choices

## Abstract

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parametrization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justify our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.