Computing-Eigenfrequencies-using-Finite-Element-Methods-Code/evsolver.py at main · shirnschall/Computing-Eigenfrequencies-using-Finite-Element-Methods-Code · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
from ngsolve.la import EigenValues_Preconditioner
from geometry import *


import netgen.gui
import netgen.geom2d as geom2d
from netgen.csg import *
from netgen.geom2d import unit_square
from ngsolve import *
import math
import scipy.linalg
from scipy import random
from netgen.NgOCC import *
from numpy import linalg as la
import time

# finding eigenvalues of   A u = lambda C u
# condition number = largest/smallest
class EVSolver():

    def __init__(self):
        pass

    def getF(self,l,shift=0):
        return (sqrt(abs(l - shift)) / (2 * math.pi))


    def lobpsd(self, geo , num, maxNumIterations=50, eps= 10e-6):
        lam = EigenValues_Preconditioner(mat=geo.A.mat, pre=geo.precond)

        u = GridFunction(geo.fes, multidim=num)

        #using multivectors for better performance
        uvecs = MultiVector(u.vec, num)
        vecs = MultiVector(u.vec, 2 * num)

        for v in vecs[0:num]:
            v.SetRandom()
        uvecs[:] = geo.precond * vecs[0:num]
        lams = Vector(num * [1])
        numIterations=0
        res=[1]*(maxNumIterations)

        #weird python do while loop
        while True:
            numIterations+=1
            vecs[0:num] = geo.A.mat * uvecs - (geo.M.mat * uvecs).Scale(lams)
            vecs[num:2 * num] = geo.precond * vecs[0:num]

            # T-norm res
            r = InnerProduct(vecs[num], vecs[0])
            for i in range(1, num):
                tmp = InnerProduct(vecs[num + i], vecs[i])
                if (r < tmp):
                    r = tmp
            res[numIterations-1] = r

            vecs[0:num] = uvecs

            vecs.Orthogonalize()

            asmall = InnerProduct(vecs, geo.A.mat * vecs)
            msmall = InnerProduct(vecs, geo.M.mat * vecs)

            ev, evec = scipy.linalg.eigh(a=asmall, b=msmall)
            prev = lams
            lams = Vector(ev[0:num])
            print(numIterations, ":", [self.getF(l, geo.shift) for l in lams])
            print("res:", res[numIterations-1],"\n")

            uvecs[:] = vecs * Matrix(evec[:, 0:num])


            if(abs(res[numIterations-1]) < eps or numIterations>=maxNumIterations):
                break

        for j in range(num):
            u.vecs[j][:] = 0.0
            u.vecs[j].data += uvecs[j]

        Draw(u, geo.mesh, "mode")
        SetVisualization(deformation=True)
        return ev,evec,res


    def lobpcg(self, geo , num, maxNumIterations=50, eps= 10e-6):
        lam = EigenValues_Preconditioner(mat=geo.A.mat, pre=geo.precond)

        u = GridFunction(geo.fes, multidim=num)

        # using multivectors for better performance
        uvecs = MultiVector(u.vec, num)
        vecs = MultiVector(u.vec, 2 * num)

        for v in vecs[0:num]:
            v.SetRandom()
        uvecs[:] = geo.precond * vecs[0:num]
        lams = Vector(num * [1])
        numIterations = 0
        res=[1]*(maxNumIterations)

        # weird python do while loop
        while True:
            numIterations += 1
            vecs[0:num] = geo.A.mat * uvecs[0:num] - (geo.M.mat * uvecs[0:num]).Scale(lams)
            vecs[num:2 * num] = geo.precond * vecs[0:num]

            # T-norm res
            r = InnerProduct(vecs[num], vecs[0])
            for i in range(1, num):
                tmp = InnerProduct(vecs[num + i], vecs[i])
                if (r < tmp):
                    r = tmp
            res[numIterations-1] = r

            vecs[0:num] = uvecs[0:num]

            vecs.Orthogonalize()

            asmall = InnerProduct(vecs, geo.A.mat * vecs)
            msmall = InnerProduct(vecs, geo.M.mat * vecs)

            ev, evec = scipy.linalg.eigh(a=asmall, b=msmall)
            prev = lams
            lams = Vector(ev[0:num])
            print(numIterations, ":", [self.getF(l, geo.shift) for l in lams])
            print("res:", res[numIterations-1], "\n")

            if (numIterations==1):
                tmp = MultiVector(u.vec, 2 * num)
                tmp[0:2*num] = vecs
                vecs = MultiVector(u.vec, 3 * num)
                vecs[0:2*num] = tmp[0:2 * num]

            uvecs[0:num] = vecs * Matrix(evec[:, 0:num])

            #todo: use span{w^i,x^i,p^i} instead of span{w^i,x^i,x^{i-1}} for better stability
            vecs[2 * num:3 * num] = vecs[0:num]

            if (abs(res[numIterations-1]) < eps or numIterations >= maxNumIterations):
                break

        for j in range(num):
            u.vecs[j][:] = 0.0
            u.vecs[j].data += uvecs[j]

        Draw(u)
        #SetVisualization(deformation=True)
        return ev, evec, res