Related papers: High-Order Mesh r-Adaptivity with Tangential Relax…
Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…
Adaptive meshes have the potential to improve the accuracy and efficiency of atmospheric modelling by increasing resolution where it is most needed. Mesh re-distribution, or r-adaptivity, adapts by moving the mesh without changing the…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…
An equation of Monge-Amp\`ere type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…
The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint and it has been a useful method for…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
We propose an end-to-end pipeline to robustly generate high-quality, high-order and coarse quadrilateral meshes on CAD models. This kind of mesh enables the use of high-order analysis techniques such as high-order finite element methods or…