These pages were created on 04/07/2025 at 18:39:20. The latest revision of this manual is available online.

IgANets (Isogeometric Analysis Networks) is a C++ library that combines Isogeometric Analysis with deep operator learning. It builds upon the C++ API of the Torch library and is written in C++20. The library aims to provide an easy to use, user-friendly and yet computationally efficient framework for implementing IgANet applications.

The library is licenced under the Mozilla Public License Version 2.0.

Getting started

Documentation

The list of Examples
The list of PerfTests
The list of UnitTests
The list of WebApps

Mathematical notation

IgANets adopts the following mathematical symbols and notation conventions.

B-Spline basis functions

\( \xi_d \) is the value of the parametric coordinate in the \( d \)-th parametric dimension
\( \boldsymbol{\xi} = \left( \xi_1, \dots, \xi_{d_\text{par}} \right)^\top \) is the vector of parametric coordinates in all parametric dimension
\( B_{i_d,p_d}(\xi_d) \) is the \( i_d \)-th univariate B-spline basis function in the \( d \)-th parametric dimension evaluated at \( \xi_d \)
\( B_I(\boldsymbol{\xi}) = \bigotimes_{d=1}^{d_\text{par}} B_{i_d,p_d}(\xi_d) \) is the \( I \)-th multivariate B-spline basis function
\( d_\text{geo} \) is the total number of geometric dimension
\( d_\text{par} \) is the total number of parametric dimension
\( i_d \) is local index refering to the \( d \)-th dimension
\( \mathbf{i} = \left(i_1, \dots, i_d \right) \) is a local multi-index
\( I \) is a global index
\( n_d \) is the number of univariate B-spline basis functions in the \( d \)-th dimension
\( N = n_1\cdot \dots \cdot n_{d_\text{par}} \) is the total number of multivariable B-splines basis functions

B-Spline function spaces

\( S^{p}_{\boldsymbol{\alpha}} = \text{span} \left\{ B_{i,p} \right\}_{i=1}^n \) is the function space that is spanned by a univariate B-spline basis of degree \( p \) and regularity vector \( \boldsymbol{\alpha} = \left(\alpha_1, \dots, \alpha_n\right) \). By default, we assume maximal regularity, i.e. \( \alpha_i = p-1 \) for all \( i = 1, \dots, n \)
\( S^{p_1,\dots,p_{d_\text{par}}}_{\boldsymbol{\alpha}_1,\dots,\boldsymbol{\alpha}_{d_\text{par}}} \) is the function space that is spanned by a multivariate B-spline basis of degree \( \mathbf{p} = \left(p_1, \dots, p_{d_\text{par}}\right) \) with regularity vectors \( \boldsymbol{\alpha}_d \) for each parametric dimension \( d = 1, \dots d_\text{par} \). By default, we assume maximal regularity (see above)

Getting started

Documentation

Mathematical notation

B-Spline basis functions

B-Spline function spaces

Copyright