Finite-Element-Method-(FEM)(ppt文档).ppt

Finite Element Method(FEM)BELA:Finite Element Electrostatic SolverFEMM:Finite Element Method Magnetics5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024BELA:IntroductionPlasma ApplicationModeling GroupPOSTECHBELA and FEMM are freeware software packages for 2D analysis of electrostatic and magnetostatic linear problems.These packages were written by David Meeker.The homepage is located at:http:/femm.foster-5/25/2024BELA:Triangle Plasma ApplicationModeling GroupPOSTECHTriangle is a 2D mesh generator and Delaunay Triangulator.It was written by Jonathan Shewchuk.The homepage:http:/www-2.cs.cmu.edu/quake/triangle.htmlWinner of the 2003 James Hardy WilkinsonPrize in Numerical Software5/25/2024BELA:Boundary ConditionsPlasma ApplicationModeling GroupPOSTECHDirichlet,the value is explicitly defined on the boundary,e.g.Neumann,the normal derivative is defined on the boundary,e.g.Mixed,If no boundary conditions are defined,Neumann BC is used.5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024BELA:Geometry of the ProblemPlasma ApplicationModeling GroupPOSTECHProblem Type:Planar or AxisymmetricLength Units:mils,micrometers,millimeters,centimeters,inches,and meters5/25/2024BELA:Geometry of the ProblemPlasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Object Properties(1)Plasma ApplicationModeling GroupPOSTECHBoundary Properties:Fixed VoltageMixedSurface Charge DensityPeriodicAntiperiodicMaterials Library5/25/2024BELA:Object Properties(2)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Object Properties(3)Plasma ApplicationModeling GroupPOSTECH5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024BELA:Mesh and SolverPlasma ApplicationModeling GroupPOSTECH5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024BELA:ResultsPlasma ApplicationModeling GroupPOSTECHContour PlotDensity Plots:Voltage(V)Electric Field Intensity(E)Electric Flux Density (D)5/25/2024BELA:Results(1)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(1)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(2)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(3)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(4)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:ResultsPlasma ApplicationModeling GroupPOSTECHLine Plots:Potential along the contour Magnitude of the flux density along the contour(|D|)Component of flux normal to the contour(D.n)Component of flux density tangential to the contour(D.t)Magnitude of the field intensity along the contour(|E|)Component field intensity normal to the contour(E.n)Component of field intensity tangential to the contour(E.t)5/25/2024BELA:Results(5)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(5)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(6)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Results(6)Plasma ApplicationModeling GroupPOSTECH5/25/2024BELA:ResultsPlasma ApplicationModeling GroupPOSTECHLine Integrals:Voltage drop along the contour(E.t)Total electric flux passing through the contour(D.n).If the contour is closed,the result is equal to the charge inside this contour Contour Length and/or Area Force from stress tensor Torque from stress tensor5/25/2024BELA:ResultsPlasma ApplicationModeling GroupPOSTECHBlock Integrals:Storage Energy Block cross-section area Block Volume Average E over the volume Average D over the volume5/25/2024BELA:Results(7)Plasma ApplicationModeling GroupPOSTECH5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024BELA:Example One QuarterPlasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Example One QuarterPlasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Example One QuarterPlasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Example CirclePlasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Example CirclePlasma ApplicationModeling GroupPOSTECH5/25/2024BELA:Example CirclePlasma ApplicationModeling GroupPOSTECH5/25/2024ContentsPlasma ApplicationModeling GroupPOSTECHIntroduction to BELA and FEMM packagesStep 1.Drawing the problem geometryStep 2.Solve the problemStep 3.Results analysisSome more examplesNumerical methods5/25/2024BELA:Numerical MethodsPlasma ApplicationModeling GroupPOSTECHGeneral description of the finite element method:Step 1.The problem is discretized by dividing the total space domain into simple subdomains,the elements.In 2D problems the basic region is divided into triangles,parallelograms or curved-sided triangles.For 3D problems the region is discretized into tetrahedral or cubic elements.5/25/2024BELA:Numerical MethodsPlasma ApplicationModeling GroupPOSTECHGeneral description of the finite element method:BELA(and FEMM)uses triangular elements with linear approximation of the potential by the expressionPotential along any triangle edge is the linear interpolate between its two vertex values,so if two triangles share the same vertices,the potential will be continuous across the interelement boundary.The linear algebra problem is formed by choosing the potential on the basis of minimizing the total energy of the problem.5/25/2024BELA:Numerical MethodsPlasma ApplicationModeling GroupPOSTECHGeneral description of the finite element method:BELA(and FEMM)uses the Cuthill-McKee method for renumbering the nodes.Source file:cuthill.cpp5/25/2024BELA:Numerical MethodsPlasma ApplicationModeling GroupPOSTECHGeneral description of the finite element method:Step 2.For each of the elements a suitable approximation to the functions which describe the problem,has to be chosen.In general the form of the trial function in the element is controlled by function value at certain points of the element,the nodes.5/25/2024BELA:Numerical MethodsPlasma ApplicationModeling GroupPOSTECHGeneral description of the finite element method:Step 3.Solving the system of equations is the final step in a FEM.Once the system of equations is solved,the desired parameters can be compute and display in for of the curves,plots,etc.This stage is often referred to as postprocessing.To solve the set of linear equations Symmetric Successive Over Relaxation(SSOR)method is used.Source file:spars.cpp5/25/2024