{"id":20500600,"url":"https://github.com/juliaapproximation/multivariateorthogonalpolynomials.jl","last_synced_at":"2025-10-18T18:58:50.826Z","repository":{"id":4930653,"uuid":"42019701","full_name":"JuliaApproximation/MultivariateOrthogonalPolynomials.jl","owner":"JuliaApproximation","description":"Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles","archived":false,"fork":false,"pushed_at":"2025-02-27T16:51:17.000Z","size":5837,"stargazers_count":18,"open_issues_count":29,"forks_count":5,"subscribers_count":9,"default_branch":"master","last_synced_at":"2025-02-27T23:27:43.655Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"","language":"Julia","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"other","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/JuliaApproximation.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE.md","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2015-09-06T21:38:27.000Z","updated_at":"2025-02-22T17:04:13.000Z","dependencies_parsed_at":"2023-10-04T04:56:44.566Z","dependency_job_id":"77de24fd-fd4a-435e-a38f-61282f9c80f3","html_url":"https://github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl","commit_stats":{"total_commits":279,"total_committers":10,"mean_commits":27.9,"dds":"0.24731182795698925","last_synced_commit":"459305480a21b76e5022f11d9a97ecab5d91830d"},"previous_names":[],"tags_count":37,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FMultivariateOrthogonalPolynomials.jl","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FMultivariateOrthogonalPolynomials.jl/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FMultivariateOrthogonalPolynomials.jl/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FMultivariateOrthogonalPolynomials.jl/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/JuliaApproximation","download_url":"https://codeload.github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":242092515,"owners_count":20070543,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-15T18:21:52.183Z","updated_at":"2025-10-18T18:58:45.794Z","avatar_url":"https://github.com/JuliaApproximation.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"# MultivariateOrthogonalPolynomials.jl\n\n[![Build Status](https://github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl/actions)\n[![codecov](https://codecov.io/gh/JuliaApproximation/MultivariateOrthogonalPolynomials.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/MultivariateOrthogonalPolynomials.jl)\n\nThis is an experimental package to add support for multivariate orthogonal polynomials on disks, spheres, triangles, and other simple\ngeometries to [ContinuumArrays.jl](https://github.com/JuliaApproximation/ContinuumArrays.jl). At the moment it primarily supports triangles. For example,\nwe can solve variable coefficient Helmholtz on the triangle with zero Dirichlet conditions as follows:\n```julia\njulia\u003e using MultivariateOrthogonalPolynomials, StaticArrays, LinearAlgebra\n\njulia\u003e P = JacobiTriangle()\nJacobiTriangle(0, 0, 0)\n\njulia\u003e x,y = coordinates(P);\n\njulia\u003e u = P * (P \\ (exp.(x) .* cos.(y))) # Expand in Triangle OPs\nJacobiTriangle(0, 0, 0) * [1.3365085377830084, 0.5687967596428205, -0.22812040274224554, 0.07733064070637755, 0.016169744493985644, -0.08714886622738759, 0.00338435674992512, 0.01220019521126353, -0.016867598915573725, 0.003930461395801074  …  ]\n\njulia\u003e u[SVector(0.1,0.2)] # Evaluate expansion\n1.083141079608063\n```\nSee the examples folder for more examples, including non-zero Dirichlet conditions, Neumann conditions, and piecing together multiple triangles. In particular, the [examples](examples/triangleexamples.jl) from Olver, Townsend \u0026 Vasil 2019.\n\n\nThis code relies on Slevinsky's [FastTransforms](https://github.com/MikaelSlevinsky/FastTransforms) C library for calculating transforms between values and coefficients. At the moment the path to the compiled FastTransforms library is hard coded in [c_transforms.jl](src/c_transforms.jl). \n\n## References\n\n\n- S. Olver, A. Townsend \u0026 G.M. Vasil (2019), [A sparse spectral method on triangles](https://arxiv.org/pdf/1902.04863.pdf), arXiv:1902.04\n- S. Olver \u0026 Y. Xuan (2019), [Orthogonal polynomials in and on a quadratic surface of revolution](https://arxiv.org/abs/1906.12305.pdf), arXiv:1906.12305\n- G.M. Vasil, K.J. Burns, D. Lecoanet, S. Olver, B.P. Brown \u0026 J.S. Oishi (2016), [Tensor calculus in polar coordinates using Jacobi polynomials](http://arxiv.org/pdf/1509.07624.pdf), J. Comp. Phys., 325: 53–73\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fmultivariateorthogonalpolynomials.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjuliaapproximation%2Fmultivariateorthogonalpolynomials.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fmultivariateorthogonalpolynomials.jl/lists"}