Finite Element Method Programming With Mathematica Pdf
- WolframAlpha.com
- WolframCloud.com
- All Sites & Public Resources...
Wolfram Language & System Documentation Center
Wolfram Language Home Page »
Finite Element Method User Guide
Solving Partial Differential Equations with Finite Elements
Introduction
Why Finite Elements?
What Is Needed for a Finite Element Analysis
The Scope of the Finite Element Method as Implemented in NDSolve
Regions
Classical Partial Differential Equations
The Coefficient Form of Partial Differential Equations
Poisson's Equation with Dirichlet Conditions
Partial Differential Equations and Boundary Conditions
Poisson's Equation with Neumann Values
Poisson's Equation with a Periodic Boundary Condition
Partial Differential Equations with Variable Coefficients
Partial Differential Equations with Nonlinear Coefficients
Partial Differential Equations with Nonlinear Variable Coefficients
Partial Differential Equations and Nonlinear Boundary Conditions
Heat Equation
Wave Equation
Formal Partial Differential Equations
Systems of Partial Differential Equations
The Coefficient Form of Systems of Partial Differential Equations
One-Dimensional Coupled Partial Differential Equation
Structural Mechanics
Fluid Flow
Element Mesh Generation
Introduction
Passing an ElementMesh to NDSolve
Passing Options for the ElementMesh Creation to NDSolve via MeshOptions
Comparing ElementMesh and MeshRegion
Approximation of Regions with ElementMesh
Manual Mesh Creation
Line Meshes
Triangle Meshes
Quad Meshes
Mixed Element Type Meshes in 2D
Boundary Meshes in 2D
Tetrahedron Meshes
Hexahedron Meshes
Mixed Element Type Meshes in 3D
Boundary Meshes in 3D
Region Approximation Quality
Element Mesh Quality
Visualize Low-Quality Elements
Numerical Regions
Element Meshes with Subregions
Markers
Element Meshes in Other Functions
Region Membership Tests
Interpolation
Element Mesh Visualization
Wireframes
Issues
Visualizing Deformations
Converting ElementMesh
Finite Element Method Usage Tips
Introduction
Monitoring the Solution Progress of Nonlinear Stationary Partial Differential Equations
Monitoring Progress of Time Integration of Transient Partial Differential Equations
Solving Memory-Intensive PDEs
Extrapolation of Solution Domains
Overshoot/Undershoot Issue for Discontinuous Coefficients
Stabilization of Convection-Dominated Equations
Stabilization of Convection-Dominated Time-Dependent Equations
The Coefficient Form of a PDE
Formal Partial Differential Equations
NeumannValue and Formal Partial Differential Equations
Efficient Evaluation of PDE Coefficients
The Relation between NeumannValue and Boundary Derivatives
Ordering of Dependent Variable Names
Verifying Solutions
Finite Element Programming
Introduction
Finite Element Data within NDSolve
Passing Finite Element Options to NDSolve
A Workflow Overview
The Partial Differential Equation Problem Setup
Stationary PDEs
Initialization Stage
Discretization Stage
Solution Stage
Post-Processing
Nonlinear PDEs
Top-Level Example
Initialization Stage
Discretization and Solution Stage
Post-Processing
The Linearization Process
Solving the Linearized PDE
Transient PDEs
Transient PDE with Stationary Coefficients and Stationary Boundary Conditions—Introduction
Transient PDE with Stationary Coefficients and Stationary Boundary Conditions
Model Order Reduction of Transient PDEs with Stationary Coefficients and Stationary Boundary Conditions
Transient PDEs with Transient Coefficients
Transient PDEs with Nonlinear Transient Coefficients
Transient PDEs with Integral Coefficients
Coupled PDEs
Deformation of a Beam under Load
A Swinging Beam—Transient Coupled PDEs
A Swinging and Dynamically Loaded Beam
Large-Scale FEM Analysis
NDSolve Options for Finite Elements
Overview
NDSolve Options
The Method Option for Solution Stages
How to Tell What Method Has Been Used
What Triggers the Use of the Finite Element Method
Finite Element Method Options for Stationary Partial Differential Equations
InitializePDECoefficients
Mesh Generation Options
PDESolveOptions
LinearSolver
FindRootOptions
Remaining "FiniteElement" Method Options
Nonlinear Finite Element Method Verification Tests
Stationary Tests
1D Single Equation
Diffusion—FEM-NL-Stationary-1D-Single-Diffusion-0001
Diffusion—FEM-NL-Stationary-1D-Single-Diffusion-0002
Convection—FEM-NL-Stationary-1D-Single-Convection-0001
Convection—FEM-NL-Stationary-1D-Single-Convection-0002
Reaction—FEM-NL-Stationary-1D-Single-Reaction-0001
Reaction—FEM-NL-Stationary-1D-Single-Reaction-0002
Reaction—FEM-NL-Stationary-1D-Single-Reaction-0003
Reaction—FEM-NL-Stationary-1D-Single-Reaction-0004
Load—FEM-NL-Stationary-1D-Single-Load-0001
Load—FEM-NL-Stationary-1D-Single-Load-0002
Radiation BC—FEM-NL-Stationary-1D-Single-Radiation-0001
Missing test types
1D Systems of Equations
Reaction—FEM-NL-Stationary-1D-System-Reaction-0001
2D Single Equation
Diffusion—FEM-NL-Stationary-2D-Single-Diffusion-0001
Reaction—FEM-NL-Stationary-2D-Single-Reaction-0001
Transient Tests
1D Single Equation
Diffusion—FEM-NL-Transient-1D-Single-Diffusion-0001
Diffusion—FEM-NL-Transient-1D-Single-Diffusion-0002
Diffusion—FEM-NL-Transient-1D-Single-Diffusion-0003
Convection—FEM-NL-Transient-1D-Single-Convection-0001
Convection—FEM-NL-Transient-1D-Single-Convection-0002
Reaction—FEM-NL-Transient-1D-Single-Reaction-0001
Reaction—FEM-NL-Transient-1D-Single-Reaction-0002
Load—FEM-NL-Transient-1D-Single-Load-0001
Load—FEM-NL-Transient-1D-Single-Load-0002
Reaction-Diffusion—FEM-NL-Transient-1D-Single-Reaction-Diffusion-0001
2D Single Equation
Diffusion—FEM-NL-Stationary-2D-Single-Diffusion-0001
Test Result Inspection
References
ReferencePages/Symbols
BoundaryConditionData
DeployBoundaryConditions
DiscretizeBoundaryConditions
DiscretizePDE
DiscretizedBoundaryConditionData
DiscretizedPDEData
ElementMesh
ElementMeshInterpolation
FEMMethodData
FiniteElementData
HexahedronElement
InitializeBoundaryConditions
InitializePDECoefficients
InitializePDEMethodData
LineElement
NumericalRegion
PDECoefficientData
PDESolve
PointElement
ProcessPDESolutions
QuadElement
TetrahedronElement
ToBoundaryMesh
ToElementMesh
ToNumericalRegion
TriangleElement
Top
Finite Element Method Programming With Mathematica Pdf
Source: https://reference.wolfram.com/language/FEMDocumentation/tutorial/FiniteElementOverview.html
Posted by: yoderfiew1977.blogspot.com
0 Response to "Finite Element Method Programming With Mathematica Pdf"
Post a Comment