1! Computes the self-capacitance of a unit cube. Only 1/8 of the cube is
2! modeled. The cube is placed within a larger cube and at the external
3! walls infinite field approximation around origin is enforced. This
4! makes it possible not to extent the mesh into infinity. Note that
5! this approximation is valid only in 3D. Permittivity of vacuum is set
6! to one to allow easier interpretation of the computed capacitance.
7!
8! As the capacitance is 1.02213 the true capacitance is something like
9! 1.02213*8*eps. This is within 2% of the exact solution.
10! Increasing mesh density and taking the outer cube further apart.
11! will improve on the accuracy.
12!
13! P.R. / 18.2.2012
14
15Check Keywords Warn
16
17Header
18  Mesh DB "." "cubes"
19End
20
21Simulation
22  Coordinate System = Cartesian 3D
23  Simulation Type = Steady State
24  Steady State Max Iterations = 1
25!  Output File = "elstatics.result"
26!  Post File = "elstatics.ep"
27End
28
29Constants
30  Permittivity Of Vacuum = 1
31!8.8542e-12
32End
33
34Body 1
35  Equation = 1
36  Material = 1
37End
38
39Equation 1
40  Active Solvers(2) = 1 2
41  Calculate Electric Energy = True
42End
43
44Solver 1
45  Equation = Stat Elec Solver
46  Variable = Potential
47  Variable DOFs = 1
48  Procedure = "StatElecSolve" "StatElecSolver"
49
50  Calculate Electric Energy = True
51  Calculate Electric Field = False
52  Calculate Electric Flux = False
53
54  Calculate Capacitance Matrix = True
55
56  Linear System Solver = Iterative
57  Linear System Iterative Method = BiCGStab
58  Linear System Max Iterations = 500
59  Linear System Convergence Tolerance = 1.0e-10
60  Linear System Preconditioning = ILU1
61  Linear System ILUT Tolerance = 1.0e-03
62  Linear System Residual Output = 10
63  Nonlinear System Max Iterations = 1
64  Nonlinear System Convergence Tolerance = 1.0e-4
65  Nonlinear System Newton After Tolerance = 1.0e-3
66  Nonlinear System Newton After Iterations = 10
67  Nonlinear System Relaxation Factor = 1
68  Steady State Convergence Tolerance = 1.0e-4
69End
70
71Solver 2
72  Equation = Electric Force
73  Procedure = "ElectricForce" "StatElecForce"
74End
75
76Solver 3
77  Exec Solver = After All
78  Equation = SaveScalars
79  Procedure = "SaveData" "SaveScalars"
80!  Filename = "scalars.dat"
81  Variable 1 = Potential
82  Operator 1 = max
83  Operator 2 = min
84End
85
86Material 1
87  Relative Permittivity = 1.0
88End
89
90Boundary Condition 1
91  Name = Bc_inner
92  Target Boundaries(2) = 2 6
93
94! The "Capacitance body" keyword automatically sets the potential.
95!  Potential = 1.0
96  Calculate Electric Force = True
97  Capacitance Body = 1
98End
99
100Boundary Condition 2
101  Name = bc_Symmetry
102  Target Boundaries(3) = 1 4 5
103End
104
105Boundary Condition 3
106  Name = bc_outer
107  Target Boundaries(2) = 3 7
108
109! Two cocentric cubes would result to Dirichlet condition for the outer cube
110! This would result to significantly larger capacitance.
111!  Potential = 0.0
112
113! This keyword enforces an approximation that assumes that the field decays as 1/r^2 to infinity
114  Electric Infinity BC = Logical True
115End
116
117Solver 1 :: Reference Norm = Real 0.482109
118RUN
119
120
121!End Of File
122
123