円環コイル電流が作る磁場¶
円環コイル電流が作る磁場の解析結果を以下に示す． 問題設定、及び、Elmer入力ファイルは、Elmer のテスト問題、及び、Elmer Discussion Forum のファイルを参考にしている．
問題設定 / メッシュ¶
半径
の円環状のコイルを考え、内部を一様に流れる直流電流が作る磁場を考える．計算領域は、円筒の計算空間を考え、とある半径
で電磁ポテンシャルは Dirichlet 条件を課す．電流として、片側 1.0 A の電流を与える．半径 0.5 m のコイルを距離 0.5 m だけ離して設置する．いわゆる Helmhortz コイルである．
円環コイル電流モデル ( 1/2モデル ver. )のメッシュ生成 プログラム¶
まずは、円筒の空気領域のうち半分の領域を考え、対称条件を課して計算する．
gmsh-API pythonを利用した円環コイル電流用メッシュの生成プログラム． 自分で作成した円筒形状生成用関数を内部で利用している．
1/2 円環コイル電流モデルのメッシュ生成用 gmsh-API python プログラム¶
1import numpy as np
2import os, sys
3import gmsh
4
5gmshlib = os.environ["gmshLibraryPath"]
6sys.path.append( gmshlib )
7
8import generate__fanShape as fan
9import generate__sectorShape as sct
10
11# ------------------------------------------------- #
12# --- [1] initialization of the gmsh --- #
13# ------------------------------------------------- #
14gmsh.initialize()
15gmsh.option.setNumber( "General.Terminal", 1 )
16gmsh.model.add( "model" )
17
18
19# ------------------------------------------------- #
20# --- [2] initialize settings --- #
21# ------------------------------------------------- #
22ptsDim , lineDim , surfDim , voluDim = 0, 1, 2, 3
23pts , line , surf , volu = {}, {}, {}, {}
24ptsPhys, linePhys, surfPhys, voluPhys = {}, {}, {}, {}
25lc = 10.0
26x_, y_, z_, lc_, tag_ = 0, 1, 2, 3, 4
27
28
29# ------------------------------------------------- #
30# --- [3] Modeling --- #
31# ------------------------------------------------- #
32
33lc_coil = 0.02
34lc_roi = 0.05
35lc_sim = 1.0
36
37simBoundary__r = 5.0
38simBoundary__z = 5.0
39roiBoundary__r = 1.0
40roiBoundary__z = 1.0
41
42rCoil1 = 0.45
43rCoil2 = 0.55
44
45th1 = 0.0
46th2 = 180.0
47gap = 0.20
48hCoil = 0.10
49
50ret1 = fan.generate__fanShape ( lc=lc_coil, r1=rCoil1, r2=rCoil2, th1=th1, th2=th2, \
51 zoffset=+gap, height=+hCoil, defineVolu=True )
52ret2 = fan.generate__fanShape ( lc=lc_coil, r1=rCoil1, r2=rCoil2, th1=th1, th2=th2, \
53 zoffset=-gap, height=-hCoil, defineVolu=True )
54
55ret3 = fan.generate__fanShape ( lc=lc_roi , r1=0.0, r2=roiBoundary__r, th1=th1, th2=th2, \
56 zoffset=-roiBoundary__z, height=2.0*roiBoundary__z, \
57 defineVolu=True )
58ret4 = fan.generate__fanShape ( lc=lc_sim , r1=0.0, r2=simBoundary__r, th1=th1, th2=th2, \
59 zoffset=-simBoundary__z, height=2.0*simBoundary__z, \
60 defineVolu=True )
61gmsh.model.occ.addPoint( 0.0, 0.0, 0.0, meshSize=lc_coil )
62gmsh.model.occ.removeAllDuplicates()
63
64volu["coil_upr"] = ret1["volu"]["fan"]
65volu["coil_lwr"] = ret2["volu"]["fan"]
66volu["roi_Area"] = ret3["volu"]["fan"]
67volu["sim_Area"] = ret4["volu"]["fan"]
68
69surf["coil_upr_in"] = 4
70surf["coil_upr_out"] = 7
71surf["coil_lwr_in"] = 12
72surf["coil_lwr_out"] = 15
73
74surf["sim_bot"] = 24
75surf["sim_side1"] = 25
76surf["sim_top"] = 26
77surf["sim_side2"] = 28
78
79surf["x=0_roi1"] = 17
80surf["x=0_roi2"] = 18
81surf["x=0_sim1"] = 23
82surf["x=0_sim2"] = 27
83
84
85# ------------------------------------------------- #
86# --- [4] Physical Grouping --- #
87# ------------------------------------------------- #
88gmsh.model.occ.synchronize()
89voluPhys["coil_upr"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["coil_upr"] ], tag=301 )
90voluPhys["coil_lwr"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["coil_lwr"] ], tag=302 )
91voluPhys["roi_Area"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["roi_Area"] ], tag=303 )
92voluPhys["sim_Area"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["sim_Area"] ], tag=304 )
93
94
95surfPhys["sim_bot"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_bot" ] ], tag=201 )
96surfPhys["sim_top"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_top" ] ], tag=202 )
97surfPhys["sim_side1"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_side1" ] ], tag=203 )
98surfPhys["sim_side2"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_side2" ] ], tag=204 )
99
100surfPhys["coil_upr_in"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_upr_in" ] ], tag=205 )
101surfPhys["coil_upr_out"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_upr_out"] ], tag=206 )
102surfPhys["coil_lwr_in"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_lwr_in" ] ], tag=207 )
103surfPhys["coil_lwr_out"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_lwr_out"] ], tag=208 )
104
105surfPhys["x=0_roi1"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["x=0_roi1" ] ], tag=209 )
106surfPhys["x=0_roi2"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["x=0_roi2" ] ], tag=210 )
107surfPhys["x=0_sim1"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["x=0_sim1" ] ], tag=211 )
108surfPhys["x=0_sim2"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["x=0_sim2" ] ], tag=212 )
109
110
111# ------------------------------------------------- #
112# --- [2] post process --- #
113# ------------------------------------------------- #
114gmsh.model.occ.synchronize()
115gmsh.model.mesh.generate(3)
116gmsh.write( "model.geo_unrolled" )
117gmsh.write( "model.msh" )
118gmsh.finalize()
119
生成用プログラムの実行は、以下の通り．
モデル生成¶
$ cd msh_half/
$ python main.py
$ ElmerGrid 14 2 model.msh
$ cd ../
$ mv msh_half/model ./
ElmerGridによって、( 14 : gmshの.mshファイル、 2 : ElmerMeshファイル4つを含んだディレクトリ )へと変換している．model.header / model.element / model.node / model.boundary が生成される．
円環コイル電流が作る磁場のElmer入力ファイル¶
以下にElmer入力ファイルのサンプルを示す．
円環コイル電流がつくる磁場の Elmer 入力ファイル ( circular_coil_half.sif )¶
1! ========================================================= !
2! === circular coil half === !
3! ========================================================= !
4
5! ------------------------------------------------- !
6! --- [1] Global Simulation Settings --- !
7! ------------------------------------------------- !
8
9CHECK KEYWORDS "Warn"
10
11Header
12 Mesh DB "." "model_half"
13 Include Path ""
14 Results Directory ""
15End
16
17Simulation
18 coordinate system = "Cartesian"
19 Coordinate Mapping(3) = 1 2 3
20
21 Simulation Type = "Steady State"
22 Steady State Max Iterations = 1
23
24 Solver Input File = "circular_coil.sif"
25 Output File = "circular_coil.dat"
26 Post File = "circular_coil.vtu"
27End
28
29Constants
30 Permeability of Vacuum = 1.2566e-06
31End
32
33! ------------------------------------------------- !
34! --- [2] Body & Material Settings --- !
35! ------------------------------------------------- !
36
37Body 1
38 Target Bodies(2) = 301 302
39 Name = "coil"
40
41 Equation = 1
42 Material = 1
43 Body Force = 1
44End
45
46Body 2
47 Target Bodies(2) = 303 304
48 Name = "Air"
49
50 Equation = 2
51 Material = 2
52End
53
54
55Material 1
56 Name = "Metal"
57 Electric Conductivity = 5.0e4
58 Relative Permittivity = 1.0
59 Relative Permeability = 1.0
60End
61
62Material 2
63 Name = "Air"
64 Electric Conductivity = 0.0
65 Relative Permittivity = 1.0
66 Relative Permeability = 1.0
67End
68
69
70! ------------------------------------------------- !
71! --- [3] Equation & Solver Settings --- !
72! ------------------------------------------------- !
73
74Equation 1
75 Name = "MagneticField_in_Coil"
76 Active Solvers(3) = 1 2 3
77End
78
79Equation 2
80 Name = "MagneticField_in_Air"
81 Active Solvers(2) = 2 3
82End
83
84
85Solver 1
86 Equation = "CoilSolver"
87 Procedure = "CoilSolver" "CoilSolver"
88
89 Linear System Solver = "Iterative"
90 Linear System Preconditioning = "ILU1"
91 Linear System Max Iterations = 1000
92 Linear System Convergence Tolerance = 1e-08
93 Linear System Iterative Method = "BiCGStabL"
94 Linear System Residual Output = 20
95 Steady State Convergence Tolerance = 1e-06
96 Linear System Symmetric = True
97
98 Desired Coil Current = Real 2.0
99 Nonlinear System Consistent Norm = True
100End
101
102Solver 2
103 Equation = "WhitneySolver"
104 Procedure = "MagnetoDynamics" "WhitneyAVSolver"
105 Variable = String "AV"
106 Variable Dofs = 1
107
108 Linear System Solver = "Iterative"
109 Linear System Iterative Method = "BiCGStab"
110 Linear System Max Iterations = 3000
111 Linear System Convergence Tolerance = 1.0e-5
112 Linear System Preconditioning = "None"
113 Linear System Symmetric = True
114End
115
116Solver 3
117 Equation = "MGDynamicsCalc"
118 Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
119 Potential Variable = String "AV"
120
121 Calculate Current Density = Logical True
122 Calculate Magnetic Field Strength = Logical True
123
124 Steady State Convergence Tolerance = 0
125 Linear System Solver = "Iterative"
126 Linear System Preconditioning = None
127 Linear System Residual Output = 0
128 Linear System Max Iterations = 5000
129 Linear System Iterative Method = "CG"
130 Linear System Convergence Tolerance = 1.0e-8
131 Linear System Symmetric = True
132
133 Calculate Nodal Fields = Logical False
134 Impose Body Force Potential = Logical True
135 Impose Body Force Current = Logical True
136 Discontinuous Bodies = True
137End
138
139
140! ------------------------------------------------- !
141! --- [4] Body Forces / Initial Conditions --- !
142! ------------------------------------------------- !
143
144Body Force 1
145! -- Give the driving external potential -- !
146 Electric Potential = Equals "CoilPot"
147End
148
149
150! ------------------------------------------------- !
151! --- [5] Boundary Conditions --- !
152! ------------------------------------------------- !
153
154Boundary Condition 1
155 Name = "Far Boundary"
156 Target Boundaries(4) = 201 202 203 204
157 AV {e} = 0.0
158End
159
160Boundary Condition 2
161 Name = "current in"
162 Target Boundaries(2) = 205 207
163 Coil End = True
164 AV {e} = 0.0
165End
166
167Boundary Condition 3
168 Name = "current out"
169 Target Boundaries(2) = 206 208
170 Coil Start = True
171 AV {e} = 0.0
172End
173
174Boundary Condition 4
175 Name = "x=0 Boundary"
176 Target Boundaries(4) = 209 210 211 212
177 AV {e} = 0.0
178End
円環コイルがつくる磁場計算（1/2モデル）の入力ファイルの要点は以下である．
解いた電磁ポテンシャルから電磁場を計算するために、 MagnetoDynamicsCalcFields を使用する．
磁場計算には WhitneyAVSolver を用いる． これは、電磁ポテンシャルを統一的に解くソルバ．
コイル電流は CoilSolver を使用して計算する． CoilSolver は、要素内部の電流連続の式を解くソルバ．コイル電流はある境界から流入し、別の境界から流出していくことになる．簡易的にコイル電流を生成するために、以下の設定を用いる．
コイル電流の値は、ソルバ内の Desired Coil Current により指定する．電流逆向きにするためには、Coil の Start/End を逆にするか、電流を負として設定する．
Body Force にて、電流源を設定する． Electric Potential として、"CoilPot" を指定する．
Boundary Condition として、 Coil Start / Coil End を指定する．
円環コイル電流がつくる磁場の解析結果¶
解析実行結果は以下に示す．以下に電流密度分布と軸方向の磁束密度を示す．
軸方向の磁束密度、及び、 z 軸方向の1次元分布を示す．
Helmhortz コイルが中心位置につくる磁場は、次のように計算される．
この値は、上記した z 軸方向の1次元分布の値と一致している．
円環コイル電流モデル ( フルモデル ver. )のメッシュ生成 プログラム¶
次に、円筒の空気領域の全領域を考えたフルモデルの生成プログラムを以下に示す．
円環コイル電流モデル（フルモデル）のメッシュ生成用 gmsh-API python プログラム¶
1import numpy as np
2import os, sys
3import gmsh
4
5gmshlib = os.environ["gmshLibraryPath"]
6sys.path.append( gmshlib )
7
8import generate__fanShape as fan
9import generate__sectorShape as sct
10
11# ------------------------------------------------- #
12# --- [1] initialization of the gmsh --- #
13# ------------------------------------------------- #
14gmsh.initialize()
15gmsh.option.setNumber( "General.Terminal", 1 )
16gmsh.model.add( "model" )
17
18
19# ------------------------------------------------- #
20# --- [2] initialize settings --- #
21# ------------------------------------------------- #
22ptsDim , lineDim , surfDim , voluDim = 0, 1, 2, 3
23pts , line , surf , volu = {}, {}, {}, {}
24ptsPhys, linePhys, surfPhys, voluPhys = {}, {}, {}, {}
25lc = 10.0
26x_, y_, z_, lc_, tag_ = 0, 1, 2, 3, 4
27
28
29# ------------------------------------------------- #
30# --- [3] Modeling --- #
31# ------------------------------------------------- #
32
33lc_coil = 0.02
34lc_roi = 0.05
35lc_sim = 1.00
36
37simBoundary__r = 5.0
38simBoundary__z = 5.0
39roiBoundary__r = 1.0
40roiBoundary__z = 1.0
41
42rCoil1 = 0.45
43rCoil2 = 0.55
44
45th1 = 0.0
46th2 = 180.0
47gap = 0.20
48hCoil = 0.10
49
50ret1 = fan.generate__fanShape ( lc=lc_coil, r1=rCoil1, r2=rCoil2, th1=th1, th2=th2, \
51 zoffset=+gap, height=+hCoil, defineVolu=True, side="+" )
52ret2 = fan.generate__fanShape ( lc=lc_coil, r1=rCoil1, r2=rCoil2, th1=th1, th2=th2, \
53 zoffset=+gap, height=+hCoil, defineVolu=True, side="-" )
54ret3 = fan.generate__fanShape ( lc=lc_coil, r1=rCoil1, r2=rCoil2, th1=th1, th2=th2, \
55 zoffset=-gap, height=-hCoil, defineVolu=True, side="+" )
56ret4 = fan.generate__fanShape ( lc=lc_coil, r1=rCoil1, r2=rCoil2, th1=th1, th2=th2, \
57 zoffset=-gap, height=-hCoil, defineVolu=True, side="-" )
58
59ret5 = fan.generate__fanShape ( lc=lc_roi , r1=0.0, r2=roiBoundary__r, th1=th1, th2=th2, \
60 zoffset=-roiBoundary__z, height=2.0*roiBoundary__z, \
61 defineVolu=True, side="+" )
62ret6 = fan.generate__fanShape ( lc=lc_roi , r1=0.0, r2=roiBoundary__r, th1=th1, th2=th2, \
63 zoffset=-roiBoundary__z, height=2.0*roiBoundary__z, \
64 defineVolu=True, side="-" )
65ret7 = fan.generate__fanShape ( lc=lc_sim , r1=0.0, r2=simBoundary__r, th1=th1, th2=th2, \
66 zoffset=-simBoundary__z, height=2.0*simBoundary__z, \
67 defineVolu=True, side="+" )
68ret8 = fan.generate__fanShape ( lc=lc_sim , r1=0.0, r2=simBoundary__r, th1=th1, th2=th2, \
69 zoffset=-simBoundary__z, height=2.0*simBoundary__z, \
70 defineVolu=True, side="-" )
71
72gmsh.model.occ.addPoint( 0.0, 0.0, 0.0, meshSize=lc_coil )
73gmsh.model.occ.removeAllDuplicates()
74
75volu["coil_upr1"] = ret1["volu"]["fan"]
76volu["coil_upr2"] = ret2["volu"]["fan"]
77volu["coil_lwr1"] = ret3["volu"]["fan"]
78volu["coil_lwr2"] = ret4["volu"]["fan"]
79volu["roi_Area1"] = ret5["volu"]["fan"]
80volu["roi_Area2"] = ret6["volu"]["fan"]
81volu["sim_Area1"] = ret7["volu"]["fan"]
82volu["sim_Area2"] = ret8["volu"]["fan"]
83
84surf["sim_top1"] = 38
85surf["sim_bot1"] = 36
86surf["sim_bot2"] = 41
87surf["sim_top2"] = 43
88surf["sim_side1"] = 37
89surf["sim_side2"] = 40
90surf["sim_side3"] = 44
91surf["sim_side4"] = 42
92
93surf["coil_upr_in"] = 45
94surf["coil_upr_out"] = 46
95surf["coil_lwr_in"] = 47
96surf["coil_lwr_out"] = 48
97
98# ------------------------------------------------- #
99# --- [4] Physical Grouping --- #
100# ------------------------------------------------- #
101gmsh.model.occ.synchronize()
102voluPhys["coil_upr1"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["coil_upr1"] ], tag=301 )
103voluPhys["coil_upr2"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["coil_upr2"] ], tag=302 )
104voluPhys["coil_lwr1"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["coil_lwr1"] ], tag=303 )
105voluPhys["coil_lwr2"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["coil_lwr2"] ], tag=304 )
106voluPhys["roi_Area1"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["roi_Area1"] ], tag=305 )
107voluPhys["roi_Area2"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["roi_Area2"] ], tag=306 )
108voluPhys["sim_Area1"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["sim_Area1"] ], tag=307 )
109voluPhys["sim_Area2"] = gmsh.model.addPhysicalGroup( voluDim, [ volu["sim_Area2"] ], tag=308 )
110
111surfPhys["sim_bot1"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_bot1" ] ], tag=201 )
112surfPhys["sim_bot2"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_bot2" ] ], tag=202 )
113surfPhys["sim_top1"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_top1" ] ], tag=203 )
114surfPhys["sim_top2"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_top2" ] ], tag=204 )
115surfPhys["sim_side1"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_side1"] ], tag=205 )
116surfPhys["sim_side2"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_side2"] ], tag=206 )
117surfPhys["sim_side3"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_side3"] ], tag=207 )
118surfPhys["sim_side4"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["sim_side4"] ], tag=208 )
119
120surfPhys["coil_upr_in"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_upr_in" ] ], tag=209 )
121surfPhys["coil_upr_out"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_upr_out"] ], tag=210 )
122surfPhys["coil_lwr_in"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_lwr_in" ] ], tag=211 )
123surfPhys["coil_lwr_out"] = gmsh.model.addPhysicalGroup( surfDim, [ surf["coil_lwr_out"] ], tag=212 )
124
125# ------------------------------------------------- #
126# --- [2] post process --- #
127# ------------------------------------------------- #
128gmsh.model.occ.synchronize()
129gmsh.model.mesh.generate(3)
130gmsh.write( "model.geo_unrolled" )
131gmsh.write( "model.msh" )
132gmsh.finalize()
133
円環コイル電流が作る磁場のElmer入力ファイル (フルモデル用)¶
以下にフルモデル用のElmer入力ファイルのサンプルを示す．
円環コイル電流がつくる磁場の Elmer 入力ファイル ( circular_coil_full.sif )¶
1! ========================================================= !
2! === circular coil half === !
3! ========================================================= !
4
5! ------------------------------------------------- !
6! --- [1] Global Simulation Settings --- !
7! ------------------------------------------------- !
8
9CHECK KEYWORDS "Warn"
10
11Header
12 Mesh DB "." "model_full"
13 Include Path ""
14 Results Directory ""
15End
16
17Simulation
18 coordinate system = "Cartesian"
19 Coordinate Mapping(3) = 1 2 3
20
21 Simulation Type = "Steady State"
22 Steady State Max Iterations = 1
23
24 Solver Input File = "circular_coil.sif"
25 Output File = "circular_coil.dat"
26 Post File = "circular_coil.vtu"
27End
28
29
30Constants
31 Permeability of Vacuum = 1.2566e-06
32End
33
34
35! ------------------------------------------------- !
36! --- [2] Body & Material Settings --- !
37! ------------------------------------------------- !
38
39Body 1
40 Target Bodies(2) = 301 302
41 Name = "coil1"
42
43 Equation = 1
44 Material = 1
45 Body Force = 1
46End
47
48Body 2
49 Target Bodies(2) = 303 304
50 Name = "coil2"
51
52 Equation = 1
53 Material = 1
54 Body Force = 1
55End
56
57Body 3
58 Target Bodies(4) = 305 306 307 308
59 Name = "Air"
60
61 Equation = 2
62 Material = 2
63End
64
65
66Material 1
67 Name = "Metal"
68 Electric Conductivity = 5.0e4
69 Relative Permittivity = 1.0
70 Relative Permeability = 1.0
71End
72
73Material 2
74 Name = "Air"
75 Electric Conductivity = 0.0
76 Relative Permittivity = 1.0
77 Relative Permeability = 1.0
78End
79
80
81Component 1
82 Name = "Coil1"
83 Coil Type = "test"
84 Master Bodies(1) = 1
85 ! Desired Current Density = Real -1.0e3
86 Desired Coil Current = +1.0
87End
88
89Component 2
90 Name = "Coil2"
91 Coil Type = "test"
92 Master Bodies(1) = 2
93 ! Desired Current Density = Real 1.0e3
94 Desired Coil Current = -1.0
95End
96
97
98! ------------------------------------------------- !
99! --- [3] Equation & Solver Settings --- !
100! ------------------------------------------------- !
101
102Equation 1
103 Name = "MagneticField_in_Coil"
104 Active Solvers(3) = 1 2 3
105End
106
107Equation 2
108 Name = "MagneticField_in_Air"
109 Active Solvers(2) = 2 3
110End
111
112
113Solver 1
114 Equation = "CoilSolver"
115 Procedure = "CoilSolver" "CoilSolver"
116
117 Linear System Solver = "Iterative"
118 Linear System Preconditioning = "ILU1"
119 Linear System Max Iterations = 1000
120 Linear System Convergence Tolerance = 1e-08
121 Linear System Iterative Method = "BiCGStabL"
122 Linear System Residual Output = 20
123 Steady State Convergence Tolerance = 1e-06
124
125 Optimize Bandwidth = True
126 Nonlinear System Consistent Norm = True
127 Coil Closed = Logical True
128 Narrow Interface = Logical False
129
130 Normalize Coil Current = Logical True
131 Save Coil Set = Logical True
132 Save Coil Index = Logical True
133 Calculate Elemental Fields = Logical True
134End
135
136Solver 2
137 Equation = "WhitneySolver"
138 Variable = "AV"
139 Variable Dofs = 1
140 Procedure = "MagnetoDynamics" "WhitneyAVSolver"
141
142 Linear System Solver = "Iterative"
143 Linear System Iterative Method = "BiCGStab"
144 Linear System Max Iterations = 3000
145 Linear System Convergence Tolerance = 1.0e-5
146 Linear System Preconditioning = "None"
147 Linear System Symmetric = True
148End
149
150Solver 3
151 Equation = "MGDynamicsCalc"
152 Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
153 Potential Variable = String "AV"
154
155 Calculate Current Density = Logical True
156 Calculate Electric Field = Logical False
157 Calculate Magnetic Field Strength = Logical True
158 Calculate Joule Heating = Logical False
159
160 Steady State Convergence Tolerance = 0
161 Linear System Solver = "Iterative"
162 Linear System Preconditioning = None
163 Linear System Residual Output = 0
164 Linear System Max Iterations = 5000
165 Linear System Iterative Method = "CG"
166 Linear System Convergence Tolerance = 1.0e-8
167 Linear System Symmetric = True
168
169 Nonlinear System Consistent Norm = Logical True
170 Discontinuous Bodies = True
171End
172
173
174! ------------------------------------------------- !
175! --- [4] Body Forces / Initial Conditions --- !
176! ------------------------------------------------- !
177
178Body Force 1
179 Name = "CoilCurrentSource"
180 Current Density 1 = Equals "CoilCurrent e 1"
181 Current Density 2 = Equals "CoilCurrent e 2"
182 Current Density 3 = Equals "CoilCurrent e 3"
183End
184
185
186! ------------------------------------------------- !
187! --- [5] Boundary Conditions --- !
188! ------------------------------------------------- !
189
190Boundary Condition 1
191 Name = "Far Boundary"
192 Target Boundaries(8) = 201 202 203 204 205 206 207 208
193 AV {e} = 0.0
194End
195
円環コイルがつくる磁場計算（フルモデル）の入力ファイルの要点は以下である．
1/2モデルと同様に、"WhitneyAVSolver", "MagnetoDynamicsCalcFields", "CoilSolver" を解く．
1/2モデルと異なり、フルモデルではループ電流となるため、 CoilSolver における電流の流出入がない．そこで、電流路に２枚の微小距離を離しておいた仮想的な境界面を用意し、２枚の境界面の間にポテンシャルを設定する．微小距離空隙以外の領域（長い流路側）で電流を流す．これを2つ用意してやることでループ電流をつくるらしい．これを用いるために次の設定を用いる．
Body 1 / Body 2 とコイル毎にBody指定を分け、さらに 0次元量としての電源を定義するために、 Component を各 Body に紐付けて定義する．Component 毎に Desired Coil Current を指定しておく．
CoilSolver 内に、 Coil Closed 及び、 Calculate Elemental Fields を True とする．
他、 上の戦略で電流計算するためには、 Narrow Interface を True とする、 コイル情報を示すために、 Set Coil Index , Set Coil Set を True とする． ( False でも構わない )．
Body Force として、Current Density 1,2,3 を定義する．
上記により、ループ電流を定義し、磁場を計算する．
円環コイル電流がつくる磁場の解析結果 ( フルモデル ver. )¶
解析実行結果は以下に示す．以下に電流密度分布と軸方向の磁束密度を示す．
軸方向の磁束密度、及び、 z 軸方向の1次元分布を示す．
フルモデルでも、 Helmhortz コイルのつくる磁場の理論値と一致する．
