Alvise Sommariva
Alvise Sommariva
Software in Python
In this homepage, we provide some Python versions of our Matlab open-source routines.
This effort has been done with the help of students and research associates, who also checked that these versions are numerically equivalent to the Matlab ones.
Python codes for cheap quadrature over spline curvilinear polygons and 3D domains (w.r.t. QMC based measures).
Notice that the repository contains a translation of splinegauss (algebraic cubature over spline curvilinear polygons) in Python. These rules have interior points and positive weights.
Software: GitHub (L. Rinaldi homepage)
Relevant subroutines/folders:
The .zip files contain two folder with demos that perform experiments respectively over spline curvilinear polygons and 3D complex domains.
Each folder contains in particular
demo_ADE: quadrature of polynomial integrands (to establish numerically the properties regarding the degree of exactness),
demo_CUB: quadrature of polynomial integrands,
demo_CPU: average cputimes of the rules,
demo_WEIGHTS: distribution of the weights,
demo_SUMWEIGHTS: stability of the rules.
Furthermore, a routine shows the geometry of the domain and the distribution of the nodes in a parallelepiped containing the integration domain.
PDF: Effective numerical integration on complex shaped elements by discrete signed measures , L. Rinaldi, A. Sommariva and M. Vianello
Author of the routines: L. Rinaldi
Relevant subroutines/folders: discrete_extremal_sets_constructor, discrete_orthogonal_polynomials_constructor_and_evaluator, domains_structure, demo_cpom,lebesgue_constant_evaluator,polynomial_mesh_constructor,stabilized_vandermonde_matrix_constructor,demo_cdes.py,demo_cleb.py.
PDF: CPOLYMESH, Python codes for complex polynomial approximation by Chebyshev admissible meshes
Author: D.J. Kenne
Subperiodic trigonometric quadrature and linear blending of elliptical arcs
Relevant subroutines: gauss.py, gqcircsect.py, gqcircsegm.py, trigauss.py
PDF: Python package for subperiodic trigonometric quadrature and multivariate applications
Author: M. Storgato
Quadrature on polygonal elements with a curved edge
Software: https://github.com/2002232/Squaring-polygonal-elements-with-one-curved-side-in-Python.git
Subroutines: auto_rotation.py, chebvand.py, chebyshev.py, circtrap.py, comprexcub.py, cubature_rules_1d.py, demo_polygcirc.py, gauss.py, gqellblend.py, points2distances.py, polygauss.py, polygcirc.py, r_jacobi.py, tridisolve.py, trigauss.py
PDF: G. Traversin, Python package for numerical cubature on polygonal elements with one curved edge.
Author: G. Traversin