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Wavelets Defined Over Non Nested Tetrahedral Grids: A Theoretical Approach

Liliana B. Boscardin, Silvia M. Castro, Liliana R. Castro
2019 Journal of Computer Science and Technology  
The main contribution of this paper is the definition of wavelets over non nested tetrahedral grids, allowing the representation of functions defined on an a irregular tetrahedralization.  ...  All this is within the framework of non nested tetrahedral grids.  ...  Both operators are used to simplify irregular meshes and constitute an essential stage to define wavelets over non nested tetrahedral grids.  ... 
doi:10.24215/16666038.19.e02 fatcat:zzhuhsvfsjhgxgz37tofob6zy4

Multiscale cholesky preconditioning for ill-conditioned problems

Jiong Chen, Florian Schäfer, Jin Huang, Mathieu Desbrun
2021 ACM Transactions on Graphics  
L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche  ...  HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not.  ...  CHOLESKY-BASED OPERATOR-ADAPTED WAVELETS Our new preconditioner has its theoretical roots in a homogenization approach based on operator-adapted wavelets.  ... 
doi:10.1145/3450626.3459851 fatcat:i7ok6khkgvh5rnlmx522b244ce

Simplex and Diamond Hierarchies: Models and Applications

K. Weiss, L. De Floriani
2011 Computer graphics forum (Print)  
In this state of the art report, we distinguish between approaches that focus on a specific dimension and those that apply to all dimensions.  ...  Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains.  ...  [GMC * 06] compress diamond-based clustered updates using a wavelet lifting scheme to achieve an adaptive RSB mesh with the same compression rates achieved by nested regular grid approaches [LH04] .  ... 
doi:10.1111/j.1467-8659.2011.01853.x fatcat:srj3xptopjee5p73gip7vz3w4a

Simplex and Diamond Hierarchies: Models and Applications [article]

K. Weiss, L. De Floriani
2010 Eurographics State of the Art Reports  
In this state of the art report, we distinguish between approaches that focus on a specific dimension and those that apply to all dimensions.  ...  Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains.  ...  [GMC * 06] compress diamond-based clustered updates using a wavelet lifting scheme to achieve an adaptive RSB mesh with the same compression rates achieved by nested regular grid approaches [LH04] .  ... 
doi:10.2312/egst.20101064 fatcat:acpgn3wu7fegthjkmapzbc5q5i

Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity

Frederik J. Simons, Ignace Loris, Guust Nolet, Ingrid C. Daubechies, S. Voronin, J. S. Judd, P. A. Vetter, J. Charléty, C. Vonesch
2011 Geophysical Journal International  
The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the ℓ 2 norm of the data residuals and the ℓ  ...  We propose a class of spherical wavelet bases for the analysis of geophysical models and for the tomographic inversion of global seismic data.  ...  In this flexible approach we define the grid size of the cubed sphere at the outset and we are thus able to switch between the various wavelet bases without much additional effort.  ... 
doi:10.1111/j.1365-246x.2011.05190.x fatcat:3y76j3bjkvad3kze3gtapq4iwu

Overview of Volume Rendering [chapter]

ARIE KAUFMAN, KLAUS MUELLER
2005 Visualization Handbook  
When such a grid has been non-linearly transformed while preserving the grid topology, the grid becomes curvilinear.  ...  In general, the most convenient grids for rendering purposes are tetrahedral grids and hexahedral grids.  ... 
doi:10.1016/b978-012387582-2/50009-5 fatcat:gthzcwcaanhuvhpmab7ii6r5fa

CHARMS: a simple framework for adaptive simulation

Eitan Grinspun, Petr Krysl, Peter Schröder
2002 ACM Transactions on Graphics  
In this paper we are introducing a new approach to produce conforming, hierarchical, adaptive refinement methods (CHARMS).  ...  This removes a number of implementation headaches associated with other approaches and is a general technique independent of domain dimension (here 2D and 3D), element type (e.g., triangle, quad, tetrahedron  ...  Non-adaptive approaches require a very fine grid throughout this simulation, in contrast our adaptive approach begins with a coarse mesh and adds only necessary detail.  ... 
doi:10.1145/566654.566578 fatcat:xh2dy5yagjhkzpfli2s3ykhxtm

Uncertainty Quantification For Low-Frequency Maxwell Equations With Stochastic Conductivity Models

Dimitris Kamilis, Nick Polydorides
2018 Zenodo  
In such cases, one may use a probabilistic description based on prior information and formulate a forward UQ problem of characterising the uncertainty in the PDE solution and observations in response to  ...  This work employs instead stochastic models where the conductivity is represented as a lognormal random field, with the objective of providing a more informative characterisation of the model observables  ...  For non-nested quadrature rules, these sets are constructed in each iteration as the union of product grids (eq. (4.1.7)) associated to selected indices .  ... 
doi:10.5281/zenodo.1243753 fatcat:xd7ktgeiz5cjbbzl3cm4jy4phq

Sparse tensor spherical harmonics approximation in radiative transfer

K. Grella, Ch. Schwab
2011 Journal of Computational Physics  
On nested, hierarchical sets of grids refined up to a level l, sets of basis functions which preserve this hierarchical property are defined so that each set of functions can be associated with the level  ...  For finite element spaces with an underlying grid, the framework of sparse grids (Bungartz and Griebel 2004) provides an approach to reduce the number of basis functions without compromising accuracy  ... 
doi:10.1016/j.jcp.2011.07.028 fatcat:wioeh73ck5e6jexw4iep6joxga

Tutorials on Adaptive multiresolution for mesh refinement applied to fluid dynamics and reactive media problems

Christian Tenaud, Max Duarte
2011 ESAIM: Proceedings and Surveys  
Pioneering works on adaptive methods like Multi-Level Adaptive Techniques (MLAT) (Brandt [10]) or Adaptive Mesh Refinement (AMR) (Berger et al [4-6]) demonstrated that a set of locally refined grids can  ...  approximations spatiales et temporelles de haute résolution,à reproduire les mécanismes physiques fondamentaux en assurant des gains substantiels, par rapportà des simulations sur un maillage unique,à  ...  Nested grid techniques have also been developed for unstructured grids [11, 28] , where triangle or tetrahedral elements are considered.  ... 
doi:10.1051/proc/201134004 fatcat:hzqzjuaqj5awlinogmme5gjhhm

Simplification, LOD and MultiresolutionPrinciples and Applications [article]

Enrico Puppo, Roberto Scopigno
1997 Eurographics State of the Art Reports  
of such a framework.  ...  The problem of approximating a surface with a triangular mesh is formally introduced, and major simplification techniques are classified, reviewed, and compared.  ...  Wavelet approaches have been proposed to manage regularly gridded meshes 42; 53 or more generic meshes 36; 8 .  ... 
doi:10.2312/egt.19971011 fatcat:6ouv5nrr6bapxiv3elfgnby6tu

ABINIT: First-principles approach to material and nanosystem properties

X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese (+21 others)
2009 Computer Physics Communications  
Every scaling function and wavelet on a coarse grid of spacing h can be expressed as a linear combination of scaling functions at the finer grid level h/2.  ...  over i 1 , i 2 , i 3 runs over all the grid points contained in the low resolution region and the sum over j 1 , j 2 , j 3 over all the points contained in the (generally smaller) high resolution region  ... 
doi:10.1016/j.cpc.2009.07.007 fatcat:a7qjwukjkfbqlpzpyfjojare6y

Space-time points: 4D splatting on efficient grids

N. Neophytou, K. Mueller
Symposium on Volume Visualization and Graphics, 2002. Proceedings. IEEE / ACM SIGGRAPH  
The slicing of a 4D BCC volume yields a 3D BCC volume, which theoretically has 70% of the datapoints of an equivalent CC volume. We reach compressions close to this in practice.  ...  In this paper, we explore the use of 4D Body Centered Cubic (BCC) grids to provide a more efficient sampling lattice.  ...  We would like to thank Kwan-Liu Ma for his help in obtaining the 4D datasets, and Tom Theußl and Torsten Möller for helpful discussions on BCC grids.  ... 
doi:10.1109/swg.2002.1226515 dblp:conf/volvis/NeophytouM02 fatcat:37z4ek7ovrbjdaiue5o4ghr5ni

Real-space mesh techniques in density-functional theory

Thomas L. Beck
2000 Reviews of Modern Physics  
uniform grid.  ...  Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations.  ...  While these convergence rates are a significant improvement over steepest-descent iterations, they are non-optimal due to the linearization in their method (see below).  ... 
doi:10.1103/revmodphys.72.1041 fatcat:3ndp2nv6ubhohidetdwizdwmlm

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  Our objective is to simulate transport processes over very long time periods, as needed in, e.g., the simulation of geologic carbon sequestration.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi
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