Mimetic Operators Library Enhanced 4.0
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Public Member Functions | List of all members
Divergence Class Reference

#include <divergence.h>

Inheritance diagram for Divergence:
Inheritance graph
[legend]

Public Member Functions

 Divergence (u16 k, u32 m, Real dx)
 
 Divergence (u16 k, u32 m, u32 n, Real dx, Real dy)
 
 Divergence (u16 k, u32 m, u32 n, u32 o, Real dx, Real dy, Real dz)
 
vec getQ ()
 

Detailed Description

Definition at line 7 of file divergence.h.

Constructor & Destructor Documentation

◆ Divergence() [1/3]

Divergence::Divergence ( u16 k,
u32 m,
Real dx )

Definition at line 4 of file divergence.cpp.

4 : sp_mat(m+2, m+1)
5{
6 assert(!(k%2));
7 assert(k > 1 && k < 7);
8 assert(m > 2*k);
9
10 switch (k) {
11 case 2:
12 for (u32 i = 1; i < m+1; i++) {
13 at(i, i-1) = -1.0;
14 at(i, i) = 1.0;
15 }
16 // Weights
17 Q << 1.0 << 1.0 << 1.0 << 1.0 << 1.0;
18 break;
19 case 4:
20 // A
21 at(1, 0) = -11.0/12.0;
22 at(1, 1) = 17.0/24.0;
23 at(1, 2) = 3.0/8.0;
24 at(1, 3) = -5.0/24.0;
25 at(1, 4) = 1.0/24.0;
26 // A'
27 at(m, m) = 11.0/12.0;
28 at(m, m-1) = -17.0/24.0;
29 at(m, m-2) = -3.0/8.0;
30 at(m, m-3) = 5.0/24.0;
31 at(m, m-4) = -1.0/24.0;
32 // Middle
33 for (u32 i = 2; i < m; i++) {
34 at(i, i-2) = 1.0/24.0;
35 at(i, i-1) = -9.0/8.0;
36 at(i, i) = 9.0/8.0;
37 at(i, i+1) = -1.0/24.0;
38 }
39 // Weights
40 //
41 Q << 2186.0/1943.0 << 2125.0/2828.0 << 1441.0/1240.0 << 648.0/673.0
42 << 349.0/350.0 << 648.0/673.0 << 1441.0/1240.0 << 2125.0/2828.0
43 << 2186.0/1943.0;
44 break;
45 case 6:
46 // A
47 at(1, 0) = -1627.0/1920.0;
48 at(1, 1) = 211.0/640.0;
49 at(1, 2) = 59.0/48.0;
50 at(1, 3) = -235.0/192.0;
51 at(1, 4) = 91.0/128.0;
52 at(1, 5) = -443.0/1920.0;
53 at(1, 6) = 31.0/960.0;
54 at(2, 0) = 31.0/960.0;
55 at(2, 1) = -687.0/640.0;
56 at(2, 2) = 129.0/128.0;
57 at(2, 3) = 19.0/192.0;
58 at(2, 4) = -3.0/32.0;
59 at(2, 5) = 21.0/640.0;
60 at(2, 6) = -3.0/640.0;
61 // A'
62 at(m, m) = 1627.0/1920.0;
63 at(m, m-1) = -211.0/640.0;
64 at(m, m-2) = -59.0/48.0;
65 at(m, m-3) = 235.0/192.0;
66 at(m, m-4) = -91.0/128.0;
67 at(m, m-5) = 443.0/1920.0;
68 at(m, m-6) = -31.0/960.0;
69 at(m-1, m) = -31.0/960.0;
70 at(m-1, m-1) = 687.0/640.0;
71 at(m-1, m-2) = -129.0/128.0;
72 at(m-1, m-3) = -19.0/192.0;
73 at(m-1, m-4) = 3.0/32.0;
74 at(m-1, m-5) = -21.0/640.0;
75 at(m-1, m-6) = 3.0/640.0;
76 // Middle
77 for (u32 i = 3; i < m-1; i++) {
78 at(i, i-3) = -3.0/640.0;
79 at(i, i-2) = 25.0/384.0;
80 at(i, i-1) = -75.0/64.0;
81 at(i, i) = 75.0/64.0;
82 at(i, i+1) = -25.0/384.0;
83 at(i, i+2) = 3.0/640.0;
84 }
85 // Weights
86 Q << 2383.0/2005.0 << 929.0/2002.0 << 887.0/531.0 << 3124.0/5901.0
87 << 1706.0/1457.0 << 457.0/467.0 << 1057.0/1061.0 << 457.0/467.0
88 << 1706.0/1457.0 << 3124.0/5901.0 << 887.0/531.0 << 929.0/2002.0
89 << 2383.0/2005.0;
90 break;
91 }
92
93 // Scaling
94 *this /= dx;
95}

◆ Divergence() [2/3]

Divergence::Divergence ( u16 k,
u32 m,
u32 n,
Real dx,
Real dy )

Definition at line 98 of file divergence.cpp.

99{
100 Divergence Dx(k, m, dx);
101 Divergence Dy(k, n, dy);
102
103 sp_mat Im = speye(m+2, m+2);
104 sp_mat In = speye(n+2, n+2);
105
106 Im.shed_col(0);
107 Im.shed_col(m);
108 In.shed_col(0);
109 In.shed_col(n);
110
111 sp_mat D1 = Utils::spkron(In, Dx);
112 sp_mat D2 = Utils::spkron(Dy, Im);
113
114 // Dimensions = (m+2)*(n+2), 2*m*n+m+n
115 if (m != n)
116 *this = Utils::spjoin_rows(D1, D2);
117 else {
118 sp_mat A1(1, 2);
119 sp_mat A2(1, 2);
120 A1(0, 0) = A2(0, 1) = 1.0;
121 *this = Utils::spkron(A1, D1) + Utils::spkron(A2, D2);
122 }
123}
Utils::spjoin_rows
static sp_mat spjoin_rows(const sp_mat &A, const sp_mat &B)
Definition utils.cpp:85
Utils::spkron
static sp_mat spkron(const sp_mat &A, const sp_mat &B)
Definition utils.cpp:53

◆ Divergence() [3/3]

Divergence::Divergence ( u16 k,
u32 m,
u32 n,
u32 o,
Real dx,
Real dy,
Real dz )

Definition at line 126 of file divergence.cpp.

127{
128 Divergence Dx(k, m, dx);
129 Divergence Dy(k, n, dy);
130 Divergence Dz(k, o, dz);
131
132 sp_mat Im = speye(m+2, m+2);
133 sp_mat In = speye(n+2, n+2);
134 sp_mat Io = speye(o+2, o+2);
135
136 Im.shed_col(0);
137 Im.shed_col(m);
138 In.shed_col(0);
139 In.shed_col(n);
140 Io.shed_col(0);
141 Io.shed_col(o);
142
143 sp_mat D1 = Utils::spkron(Utils::spkron(Io, In), Dx);
144 sp_mat D2 = Utils::spkron(Utils::spkron(Io, Dy), Im);
145 sp_mat D3 = Utils::spkron(Utils::spkron(Dz, In), Im);
146
147 // Dimensions = (m+2)*(n+2)*(o+2), 3*m*n*o+m*n+m*o+n*o
148 if ((m != n) || (n != o))
149 *this = Utils::spjoin_rows(Utils::spjoin_rows(D1, D2), D3);
150 else {
151 sp_mat A1(1, 3);
152 sp_mat A2(1, 3);
153 sp_mat A3(1, 3);
154 A1(0, 0) = A2(0, 1) = A3(0, 2) = 1.0;
155 *this = Utils::spkron(A1, D1) + Utils::spkron(A2, D2) + Utils::spkron(A3, D3);
156 }
157}

Member Function Documentation

◆ getQ()

vec Divergence::getQ ( )

Definition at line 160 of file divergence.cpp.

161{
162 return Q;
163}
The documentation for this class was generated from the following files: