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from esys.escript import *
from esys.escript.linearPDEs import LinearPDE, SolverOptions, LinearSinglePDE
import numpy as np
class SonicWaveInFrequencyDomain(object):
"""
This class is a simple wrapper for the solution of the 2D or 3D sonic wave equtaion in the frequency domain.
It solves complex PDE
div (grad p) - k^2 p = Q
where
k = omega/c
Q = source term : Dirac function
Boundary conditions implemented are NEED TO SET PML CONDITION FIRST
- perfectly matched layer : see class PMLCondition
- fixed BC - all but the top surface
It has functions
- getDomain
- setFrequency
- setVp
Output solution
- getWave
"""
def __init__(self, domain, pml_condition=None, frequency=None, vp=None, fix_boundary=True):
"""
Initialise the class with domain, boundary conditions and frequency.
Setup PDE
:param domain: the domain : setup with Dirac points
:type domain: `Domain`
:param pml_condition:
:type pml_condition:
:param frequency:
:type frequency:
:param vp: velocity field
:type vp: `Data`
:param fix_boundary: if true fix all the boundaries except the top
:type fix_boundary: `bool`
"""
Dim=domain.getDim()
self.pde=LinearPDE(domain, numEquations=1, numSolutions=1, isComplex=True)
self.pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.pml=pml_condition
if not self.pml:
self.pde.setValue(A=kronecker(domain))
self.J=1.
if fix_boundary:
x=domain.getX()
q=whereZero(x[Dim-1]-inf(x[Dim-1]))
for i in range(Dim-1):
q+=whereZero(x[i]-inf(x[i]))+whereZero(x[i]-sup(x[i]))
self.pde.setValue(q=q)
self.setFrequency(frequency)
self.setVp(vp)
def getDomain(self):
"""
returns the domain
"""
return self.pde.getDomain()
def setFrequency(self, frequency):
"""
sets the frequency
"""
self.frequency=frequency
self.newFreq=True
return self
def setVp(self, vp):
"""
sets the velocity for the rock
"""
self.newVp=True
if vp is None:
self.sigma2=None
else:
self.sigma2=1./vp**2
return self
def getWave(self, source):
"""
solve the PDE
"""
omega=self.frequency*2*np.pi
if self.pml and self.newFreq:
Dim=self.getDomain().getDim()
A=kronecker(Function(self.getDomain()))
alpha, J = self.pml.getPMLWeights(self.getDomain(), omega=omega)
for d in range(Dim):
A[d,d]=J/alpha[d]**2
self.J=J
self.pde.setValue(A=A)
if self.newFreq or self.newVp:
if self.frequency is None or self.sigma2 is None:
raise ValueError("freqency/propagation speed vp is not set.")
omega=self.frequency*2*np.pi
self.pde.setValue(D=-self.J*omega**2*self.sigma2)
self.newFreq=False
self.newVp=False
self.pde.setValue(y_dirac=source)
return self.pde.getSolution()
class PMLCondition(object):
"""
this defines the PML weights over a domain
:Lleft: thicknesses of PML to the left, bottom, front (None -> no PML)
:Lright: thicknesses of PML to the right, top, back (None -> no PML)
:return: return a mask where PML is applied.
"""
def __init__(self, sigma0=1., Lleft=[None, None, None], Lright=[None, None, None], m=3):
"""
initializes the PML pml_condition
:param sigma0: maximum PML damping
:type sigma0: `Data`
:param Lleft: thicknesses of PML to the left, bottom, front (None -> no PML)
:type Lleft: list of `floats`, length is domain dimension
:param Lright: thicknesses of PML to the right, top, back (None -> no PML)
:type Lright: list of `floats`, length is domain dimension
:param m: exponent of increase over PML layer (default 3 )
:type m: `int` or `float`
"""
self.sigma0=sigma0
self.Lleft=Lleft
self.Lright=Lright
self.m=m
def getPMLWeights(self,domain, omega):
"""
this defines the PML weights over a domain
:return: weighting alphas, J=product of alphas and J/alpha
"""
alpha=[1. ] * domain.getDim()
J=1.
X=Function(domain).getX()
for d in range(domain.getDim()):
x=domain.getX()[d]
Q=0
if self.Lleft[d] is not None:
xmin=inf(x)
Q=wherePositive(xmin+self.Lleft[d]-X[d])*((xmin+self.Lleft[d]-X[d])/self.Lleft[d])**self.m
if self.Lright[d] is not None:
xmax=sup(x)
Q=Q+wherePositive(X[d]-xmax+self.Lright[d])*((X[d]-xmax+self.Lright[d])/self.Lright[d])**self.m
alpha[d]=1-1j*self.sigma0/omega*Q
J=J*alpha[d]
return alpha, J
def getPMLMask(self,domain):
"""
returns the mask for PML layer
"""
x=domain.getX()
mask=Scalar(0., x.getFunctionSpace())
for d in range(domain.getDim()):
xx=x[d]
if self.Lleft[d] is not None:
xmin=inf(xx)
mask+=wherePositive(xmin+self.Lleft[d]-xx)
if self.Lright[d] is not None:
xmax=sup(xx)
mask+=wherePositive(xx-xmax+self.Lright[d])
return wherePositive(mask)
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