Yamyam: 1版をインポートしました

2018-06-28T20:50:25Z

1版をインポートしました

2012年7月28日 (土) 03:32にwiki>Apinzonfによる

2012-07-28T03:32:30Z

新規ページ

=== Performance Testing of Solvers ===

In this document we present the performance evaluation of some numerical solvers for our Laplacian Smooth system.

I need to solve the following system of equations.

Difusion equation for mesh smoothing:

<math>\frac{\partial V}{\partial t}=\lambda L\left( V\right) </math>

Integrating the diffusion equation with a explicit Euler scheme:

<math>\left( I+\lambda dtL\right) V^{t+1}=V^{t}</math>

Where <math>V^{t}</math> is the actual position of vertex, and <math>V^{t+1}</math> is the vertex
after smoothing.

Solving the sparse linear system

<math>Ax=b</math>

Where:

<math>A=\left( I+\lambda dtL\right) </math>

<math>x=V^{t+1}</math>

<math>b=V^{t}</math>

== Setup ==

=== Hardware Specification ===

* Processor: AMD Quad-Core 2.40 GHz

* RAM: 8.0 GB

* OS: Windows 7 Professional

* Graphics controller: NVIDIA Quadro FX 570

=== Software Specification ===

* [http://www.cgal.org/ CGAL] Computational Geometry Algorithms Library

* [http://alice.loria.fr/WIKI/index.php/Graphite/Graphite Graphite] Research platform for computer graphics

=== Numeric Solvers Used ===

* CG: Conjugate gradient method.

* BICGSTAB: Biconjugate gradient stabilized method.

* GMRES: Generalized minimal residual method.

* SUPERLU: Sparse Direct Solver, LU decomposition with partial pivoting.

* TAUCS_LLT: A library of sparse linear solvers with LLT factorization.

* TAUCS_LU: A library of sparse linear solvers with LU decomposition.

* TAUCS_LDLT: A library of sparse linear solvers with LDLT factorization.

* CHOLMOD: Supernodal sparse Cholesky factorization.

* FASTCG: Fast Conjugate gradient.

* ARPACK: Solver for symmetric matrices.

== Results ==

Numerical solver SuperLU is faster than the other methods.

The difference between the solvers is not representative.

{| {{Css/prettytable|50}}
|Model||Vertices||Edges||Faces||CG||BICGSTAB||GMRES||SUPERLU||TAUCS_LLT||TAUCS_LU||TAUCS_LDLT||CHOLMOD||FASTCG||ARPACK
|-
|cruz|| 24 || 44 || 22 || 0.05||0.05||0.04||0.04||0.05||0.04||0.05||0.05||0.05||0.50
|-
|Motionblender31|| 538 || 1608 || 1072 || 0.83||0.63||0.71||0.61||0.69||0.63||0.68||0.79||0.62||0.63
|-
|Ymodel|| 4770 || 14304 || 9536 || 19.60||16.44||16.93||16.06||16.65||17.61||16.88||17.95||18.23||16.56
|-
|mesh_0120|| 10002 || 30000 || 20000 || 33.43||27.76||29.91||28.54||29.72||31.43||29.53||30.80||30.51||30.97
|-
|neptune|| 28052 || 84168 || 56112 || 133.97||136.46||136.39||133.21||139.98||140.79||142.87||142.76||146.22||142.96
|-
|Armadillo|| 34594 || 103776 || 69184 || 194.48||174.88||175.80||169.92||179.88||174.37||181.70||183.49||183.56||185.99
|}

[[File:Apinzonf_GSOC_2012_Diagram_VerticesVsSeconds.png|center|thumb|649px|Vertices Vs Seconds ]]

← 古い版	2018年6月28日 (木) 20:50時点における版
(相違点なし)

利用者:Apinzonf/laplacian/test solvers - 版の履歴

Yamyam: 1版 をインポートしました

2012年7月28日 (土) 03:32にwiki>Apinzonfによる

Yamyam: 1版をインポートしました