Waveguide Meshes are efficient and versatile models of wave propagation along a multidimensional ideal medium. The choice of the mesh geometry affects both the computational cost and the accuracy of simulations. In this paper, we focus on 2D geometries and use multidimensional sampling theory to compare the square, triangular, and hexagonal meshes in terms of sampling efficiency and dispersion error under conditions of critical sampling. The analysis shows that the triangular geometry exhibits the most desirable tradeoff between accuracy and computational cost.
Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described physical object. This paper develops an adaptive mesh refinement strategy on trimmed geometries in the context of hierarchical B-spline based isogeometric analysis. A residual a posteriori estimator of the energy norm of the numerical approximation error is derived, in the context of the Poisson equation. The estimator is proven to be reliable, independently o…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the govern…
A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of the main complexities related to efficient and effective simulations in realistic DFMs.
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary element geometries arising in unstructured/Voronoi discretizations. Here, structured and unstructured meshes are considered and are created via Voronoi tessellation of sets of structured and unstructured seed points respectively. The novel mesh refinement procedures for both structured and unstructured meshes allow for accurate and efficient application of th…
Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation
Department of Mechanical Engineering, Indian Institute of Technology Madras（印度理工学院马德拉斯分校机械工程系）；Institute of Continuum Mechanics, Leibniz Universität Hannover（莱比锡大学汉诺威连续力学研究所）；Institute of Structural Mechanics, Bauhaus-Universität Weimar（魏玛包豪斯大学结构力学研究所）；Department of Civil and Systems Engineering, Johns Hopkins University（约翰霍普金斯大学土木与系统工程系）
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of meshes in a similar way as multigrid. The generation of body-fitted mesh hierarchies is only possible for simple geometries. On top of that, MLMC for random domains involves the generation of a mesh for every sample. Instead, here we consider the use of embedded methods which make use of simple background meshes of an artificial domain (a bounding-box) for which …
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements and more flexible adjacency relations. They can have several distinct ``generalized" vertices (or edges, faces) that occupy the same geometric position. These generalized facets are the natural degrees of freedom for classical conforming spaces of discrete differential forms appearing in finite and boundary element applications. Special attention is devoted…
High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems. Traditional SBP FD operators that approximate first-order spatial derivatives with central-difference stencils often have spurious unresolved numerical wave-modes in their computed solutions. Recently derived high order accurate upwind SBP operators based upwind FD stencils have the potential to suppress these poisonous spurious wave-modes on marginally resolved computational grids. In this paper, we demonstrate that…
