31. 有限要素方程式
( ) ( ) ( )
( )
=
=+
.pgrad,A
,A,JA,pgardArot,Arot
*
hh
*
h
*
hh
*
hhh
0
ν
Ah : Finite element approximation of A by
the Nedelec elements of simplex type,
ph : Finite element approximation of p by
the conventional piecewise linear
tetrahedral elements,
Ah
*
, ph
*
: test functions.
33. 非線形反復
Newton 法
Picard の逐次近似法
( ) ( )*
hh
*
k
n
h
n
h A,J
~
Arot,Arot =+1
ν
( )
( )
∂
∂
+=
∂
∂
+ ++
*
h
n
h
n
h
n
*
hh
*
h
n
h
n
h
n
*
h
n
h
n
h
Arot,ArotA
A
A,J
~
Arot,ArotA
A
Arot,Arot
ν
ν
ν 11
37. 有限要素方程式
Ah : Finite element approximation of A by
the Nedelec elements of simplex type,
Ah
*
: test function,
( . , . ) : the complex valued L2
-inner product.
J : an excitation current density
[A/m2
] (div J = 0 in Ω)
ω : the angular frequency [rad/s],
ν : the magnetic reluctivity [m/H],
σ : the conductivity [S/m],
i : the imaginary unit.
( ) ( ) ( ).,
~
,, ***
hhhhhh AJAAiArotArot =− ωσν
40. 有限要素方程式
=−
=+
−
.0)grad,()grad,grad(
),,
~
(),grad(
),()rot,rot(
**
**
**
hhhh
hhhh
hhhh
Ai
AJA
AAiAA
φωσφφσ
φσ
ωσν
Ah : Finite element approximation of A by
the Nedelec elements of simplex type,
φh : Finite element approximation of φ by
the conventional piecewise linear
tetrahedral elements,
Ah
*
, φh
*
: test functions,
( . , . ) : the complex valued L2
-inner product.
J : an excitation current density
[A/m2
] (div J = 0 in Ω)
ω : the angular frequency [rad/s],
ν : the magnetic reluctivity [m/H],
σ : the conductivity [S/m],
i : the imaginary unit.
63. History of residual norms
History of Residual Norms (Mesh(1))
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
1.00E+02
1.00E+03
0 100 200 300 400 500 600 700 800 900 1000
Number of iterations on the interface
ResidualNorms
Α
Α−φ