Hybrid Computing Model for Decomposed Partial Differential Equation Systems arising from Microstructural Three-Dimensional Problems

2010 ◽  
Author(s):  
K. Schrader ◽  
C. Könke
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Three Dimensional ◽  
Partial Differential ◽  
Hybrid Computing ◽  
Computing Model

Three-Dimensional Elastic Solution of a Transversely Isotropic Functionally Graded Rectangular Plate

2012 ◽  
Vol 591-593 ◽  
pp. 2655-2660 ◽  
Author(s):  
Guo Jun Nie ◽  
Zhao Yang Feng ◽  
Jun Tao Shi ◽  
Ying Ya Lu ◽  
Zheng Zhong
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Functionally Graded ◽  
Elastic Solution ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Present Solution

Three-dimensional elastic solution of a simply supported, transversely isotropic functionally graded rectangular plate is presented in this paper. Suppose that all elastic coefficients of the material have the same power-law dependence on the thickness coordinate. By introducing two new displacement functions, three equations of equilibrium in terms of displacements are reduced to two uncoupled partial differential equations. Exact solution for a second-order partial differential equation expressed by one of displacement functions is obtained and analytical solution for another fourth-order partial differential equation expressed by another displacement function is found by employing the Frobenius method. The validity of the present solution is first investigated. And the effect of the gradation of material properties on the mechanical behavior of the plate is studied through numerical examples.

A new partial differential equation for image inpainting

2021 ◽  
Vol 39 (3) ◽  
pp. 137-155
Author(s):  
Mounder Benseghir ◽  
Fatma Zohra Nouri ◽  
Pierre Clovis Tauber
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Image Inpainting ◽  
Complex Geometries ◽  
Partial Differential ◽  
Nonlinear Structure ◽  
Grey Scale ◽  
Nonlinear High Order

A considerable interest in the inpainting problem have attracted many researchers in applied mathematics community. In fact in the last decade, nonlinear high order partial dierential equations have payed a central role in high quality inpainting developments. In this paper, we propose a technique for inpainting that combines an anisotropic diusion process with an edge-corner enhancing shock ltering. This technique makes use of a partial differential equation that is based on a nonlinear structure tensor which increases the accuracy and robustness of the coupled diusion and shock ltering. A methodology of partition and adjustment is used to estimate the contrast parameters that control the strength of the diffusivity functions. We focus on restoring large missing regions in grey scale images containing complex geometries parts. Our model is extended to a three dimensional case, where numerical experimentations were carried out on lling brain multiple sclerosis lesions in medical images. The efficiency and the competitiveness of the proposed algorithm is numerically compared to other approaches on both synthetic and real images.

Three-dimensional invisible cloaks with arbitrary shapes based on partial differential equation

2010 ◽  
Vol 216 (2) ◽  
pp. 426-430 ◽  
Author(s):  
Xinhua Wang ◽  
Shaobo Qu ◽  
Zhuo Xu ◽  
Hua Ma ◽  
Jiafu Wang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Three Dimensional ◽  
Partial Differential ◽  
Arbitrary Shapes

scholarly journals Exploring Capabilities within ForTrilinos by Solving the 3D Burgers Equation

2012 ◽  
Vol 20 (3) ◽  
pp. 275-292 ◽  
Author(s):  
Karla Morris ◽  
Damian W.I. Rouson ◽  
M. Nicole Lemaster ◽  
Salvatore Filippone
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Message Passing ◽  
Message Passing Interface ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Abstract Data Type ◽  
Partial Differential ◽  
Sparse Linear Solvers ◽  
Set Up

We present the first three-dimensional, partial differential equation solver to be built atop the recently released, open-source ForTrilinos package (http://trilinos.sandia.gov/packages/fortrilinos). ForTrilinos currently provides portable, object-oriented Fortran 2003 interfaces to the C++ packages Epetra, AztecOO and Pliris in the Trilinos library and framework [ACM Trans. Math. Softw.31(3) (2005), 397–423]. Epetra provides distributed matrix and vector storage and basic linear algebra calculations. Pliris provides direct solvers for dense linear systems. AztecOO provides iterative sparse linear solvers. We demonstrate how to build a parallel application that encapsulates the Message Passing Interface (MPI) without requiring the user to make direct calls to MPI except for startup and shutdown. The presented example demonstrates the level of effort required to set up a high-order, finite-difference solution on a Cartesian grid. The example employs an abstract data type (ADT) calculus [Sci. Program.16(4) (2008), 329–339] that empowers programmers to write serial code that lower-level abstractions resolve into distributed-memory, parallel implementations. The ADT calculus uses compilable Fortran constructs that resemble the mathematical formulation of the partial differential equation of interest.

The Three-Dimensional Hollow or Solid Truncated Cone Under Axisymmetric Torsionless End Loading

1976 ◽  
Vol 43 (1) ◽  
pp. 59-63 ◽  
Author(s):  
J. L. Klemm ◽  
R. Fernandes
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Total Stress ◽  
Partial Differential ◽  
Truncated Cone ◽  
Sample Application

The Saint-Venant problems of solid or hollow truncated cone are investigated under axisymmetric torsionless end loading with the ruled sides being free from stress. Total-stress problems are formulated in terms of a vector partial differential equation whose component variables are stresses or of stress-type. A biorthogonality condition is derived which permits the numerical solution of boundary-value problems, and the results of a sample application of the method are presented.

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