TY - CHAP
T1 - Curvilinear Mesh Generation for the High-Order Virtual Element Method (VEM)
AU - Kirilov, Kaloyan
AU - Peiró, Joaquim
AU - Green, Mashy
AU - Moxey, David
AU - Beirão da Veiga, Lourenço
AU - Dassi, Franco
AU - Russo, Alessandro
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - We present a proof-of-concept methodology for generating curvilinear polygonal meshes suitable for high-order discretizations by the Virtual Element Method (VEM). A VEM discretization requires the definition of a set of boundary and internal points that are used to interpolate the approximation functions and to evaluate integrals by means of suitable quadratures. The procedure to locate these points on the boundary borrows ideas from previous work on a posteriori high-order mesh generation in which the geometrical inquiries to a B-rep of the computational domain are performed via an interface to CAD libraries. Here we describe the steps of the procedure that transforms a straight-sided polygonal mesh, generated using third-party software, into a curvilinear boundary-conforming mesh. We discuss criteria for ensuring and verifying the validity of the mesh. Finally, using the Laplace equation with Dirichlet boundary conditions as a model problem, we show that VEM discretizations on such meshes achieve the expected rates of convergence as the mesh resolution is increased.
AB - We present a proof-of-concept methodology for generating curvilinear polygonal meshes suitable for high-order discretizations by the Virtual Element Method (VEM). A VEM discretization requires the definition of a set of boundary and internal points that are used to interpolate the approximation functions and to evaluate integrals by means of suitable quadratures. The procedure to locate these points on the boundary borrows ideas from previous work on a posteriori high-order mesh generation in which the geometrical inquiries to a B-rep of the computational domain are performed via an interface to CAD libraries. Here we describe the steps of the procedure that transforms a straight-sided polygonal mesh, generated using third-party software, into a curvilinear boundary-conforming mesh. We discuss criteria for ensuring and verifying the validity of the mesh. Finally, using the Laplace equation with Dirichlet boundary conditions as a model problem, we show that VEM discretizations on such meshes achieve the expected rates of convergence as the mesh resolution is increased.
UR - http://www.scopus.com/inward/record.url?scp=85189500268&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-40594-5_19
DO - 10.1007/978-3-031-40594-5_19
M3 - Conference paper
AN - SCOPUS:85189500268
SN - 9783031405938
T3 - Lecture Notes in Computational Science and Engineering
SP - 419
EP - 439
BT - SIAM International Meshing Roundtable 2023
A2 - Ruiz-Gironés, Eloi
A2 - Sevilla, Rubén
A2 - Moxey, David
PB - Springer Science and Business Media Deutschland GmbH
T2 - SIAM International Meshing Roundtable Workshop, SIAM IMR 2023
Y2 - 6 March 2023 through 9 March 2023
ER -