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Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2019, Volume 88, Issue 316, pp. 751 - 782
The local red-green mesh refinement of consistent, simplicial meshes in d dimensions is considered. We give a constructive solution to the green closure... 
Red-green refinement | Local mesh refinement | Green closure | Simplicial meshes | Kuhn triangulation | simplicial meshes | MATHEMATICS, APPLIED | red-green refinement | green closure | FINITE-ELEMENT METHODS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2014, Volume 83, Issue 289, pp. 2161 - 2185
We study the linear finite element gradient superconvergence on special simplicial meshes which satisfy an edge pair condition. This special geometric... 
Edge patches | Superconvergence | Edge pair condition | Finite element methods | Simplicial meshes | SPACE | simplicial meshes | MATHEMATICS, APPLIED | finite element methods | edge pair condition | ERROR | edge patches | QUANTIZATION | CENTROIDAL VORONOI TESSELLATIONS | PATCH RECOVERY
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 5, pp. C471 - C503
We introduce a space-filling curve for triangular and tetrahedral red-re finement that can be computed using bitwise interleaving operations similar to the... 
Space-filling curve | Nonconforming simplicial mesh | High performance computing | Forest of octrees | Parallel adaptive mesh refinement | Morton code | REFINEMENT | FORESTS | MATHEMATICS, APPLIED | parallel adaptive mesh refinement | space-filling curve | forest of octrees | high performance computing | ALGORITHMS | nonconforming simplicial mesh
Journal Article
Computers & Graphics, ISSN 0097-8493, 05/2019, Volume 80, pp. 37 - 50
The estimation of the differential properties of a function sampled at the vertices of a discrete domain is at the basis of many applied sciences. In this... 
Discrete geometry | Simplicial meshes | Gradient estimation | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Apexes
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 6/2018, Volume 59, Issue 4, pp. 972 - 989
We provide a constructive proof of a face-to-face simplicial partition of a d-dimensional space for arbitrary d by generalizing the idea of Sommerville, used... 
Sommerville simplex | Computational Mathematics and Numerical Analysis | Sommerville tetrahedron | Shape optimization | Simplicial tessellation | Mathematics | 51M20 | Simplicial mesh | 51M04 | 51M09 | 65N50 | Combinatorics | Mesh regularity | NUMERICAL-METHOD | TILINGS | NAVIER-STOKES SYSTEM | TETRAHEDRA | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | DOMAINS | Partitions
Journal Article
Pattern Recognition Letters, ISSN 0167-8655, 2008, Volume 29, Issue 10, pp. 1571 - 1579
Journal Article
SIAM Journal on Imaging Sciences, ISSN 1936-4954, 06/2014, Volume 7, Issue 2, pp. 1263 - 1283
This paper introduces three sets of sufficient conditions for generating bijective simplicial mappings of manifold meshes. A necessary condition for a... 
Simplicial maps | Injectivity | Meshes | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | injectivity | simplicial maps | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | meshes | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Polytopes | Tasks | Tools | Collection | Mapping | Boundaries | Orientation | Optimization
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2015, Volume 275, pp. 135 - 138
We prove that both, the repeated interior point based subdivision and the LE -section of an initial -simplex in , produce a sequence of simplicial meshes with... 
Mesh refinement | Solid angle | Simplicial meshes | Simplices | SEMIGROUPS | MATHEMATICS, APPLIED | BARYCENTRIC SUBDIVISION | SHAPES | ALGORITHM | TRIANGLES
Journal Article
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, ISSN 0098-3500, 08/2019, Volume 45, Issue 3, pp. 1 - 20
We introduce the Colored Abstract Simplicial Complex library (CASC): a new, modern, and header-only C++ library that provides a data structure to represent... 
COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | molecular modeling | C plus plus library | mesh decimation | mesh generation | variadic templates | Abstract simplicial complexes
Journal Article
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 09/2000, Volume 49, Issue 1‐2, pp. 109 - 125
We present an optimization‐based approach for mesh untangling that maximizes the minimum area or volume of simplicial elements in a local submesh. These... 
mesh untangling | mesh smoothing | simplicial mesh quality | mesh improvement | Simplicial mesh quality | Mesh smoothing | Mesh untangling | Mesh improvement | MATHEMATICS, APPLIED | ENGINEERING, MULTIDISCIPLINARY | TRIANGULATIONS | GENERATION | TRANSFORMATIONS
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 11/2007, Volume 41, Issue 6, pp. 1001 - 1020
Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their... 
Higher order edge elements | Maxwell equations | Simplicial meshes | simplicial meshes | MATHEMATICS, APPLIED | BASES | FINITE-ELEMENTS | higher order edge elements | Numerical Analysis | Mathematics
Journal Article
Numerical Algorithms, ISSN 1017-1398, 2010, Volume 55, Issue 2, pp. 349 - 366
In the field of spectral element approximations, the interpolation points can be chosen on the basis of different criteria, going from the minimization of the... 
Lebesgue constant | Spectral elements | Simplicial meshes | High-order interpolation | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | TRIANGLE | FEKETE POINTS | SIMPLEX | Finite element method | Interpolation | Approximation | Constants | Spectral element method | Mathematical models | Spectra | Optimization
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2016, Volume 35, Issue 4, pp. 1 - 11
We present the Accelerated Quadratic Proxy (AQP) - a simple first-order algorithm for the optimization of geometric energies defined over triangular and... 
acceleration | simplicial meshes | optimization | first order methods | geometry | distortion | preconditioning | Geometry | Distortion | First order methods | Acceleration | Preconditioning | Simplicial meshes | Optimization | MESHES | ALGORITHM | MODEL | DEFORMATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SYSTEMS
Journal Article
ACM TRANSACTIONS ON GRAPHICS, ISSN 0730-0301, 07/2019, Volume 38, Issue 4, pp. 1 - 14
We introduce the notion of harmonic triangulations: a harmonic triangulation simultaneously minimizes the Dirichlet energy of all piecewise linear functions.... 
COMPUTER SCIENCE, SOFTWARE ENGINEERING | simplicial meshes | Dirichlet energy | ALGORITHMS | tetrahedral mesh optimization | ANGLE CONDITION
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 2011, Volume 81, Issue 10, pp. 1949 - 1961
We describe a new method for generating meshes that minimize the gradient of a discretization error. The key element of this method is construction of a tensor... 
Finite element method | Metric-based adaptation | Quasi-optimal meshes | INTERPOLATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADAPTATION | SIMPLICIAL MESHES | ERROR | GENERATION
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 02/2019, Volume 79, pp. 14 - 29
A is a recursive decomposition of space into cells that are simplices. Such a mesh is if pairs of neighboring cells meet along a single common face.... 
Compatible meshes | Hierarchical simplicial meshes | MATHEMATICS | QUADTREES | MATHEMATICS, APPLIED | Computer science
Journal Article
Mathematical Models and Computer Simulations, ISSN 2070-0482, 05/2017, Volume 9, Issue 3, pp. 377 - 382
Journal Article
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, ISSN 0927-6467, 08/2011, Volume 26, Issue 4, pp. 337 - 352
For a given function, we consider the problem of minimizing the P-1 interpolation error on a set of triangulations with a fixed number of triangles. The... 
SIMPLICIAL MESHES | MATHEMATICS, APPLIED | GENERATION | ENGINEERING, MULTIDISCIPLINARY | ADAPTATION
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2016, Volume 293, pp. 139 - 146
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 11/2015, Volume 34, Issue 6, pp. 1 - 10
Journal Article
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