def u_bound_right(x, y):
return 0.0
def u_bound_up_down(x, y):
return np.zeros_like(x)
#define the input and output data set
xmin = 0
xmax = 2
ymin = 0
ymax = 1
domainCorners = np.array([[xmin, ymin], [xmin, ymax], [xmax, ymin],
[xmax, ymax]])
myQuad = Quadrilateral(domainCorners)
numPtsU = 28
numPtsV = 28
xPhys, yPhys = myQuad.getUnifIntPts(numPtsU, numPtsV, [0, 0, 0, 0])
data_type = "float32"
Xint = np.concatenate((xPhys, yPhys), axis=1).astype(data_type)
Yint = np.zeros_like(Xint)
# Generate the training data for the Neumann boundary
xPhysNeu, yPhysNeu, xNormNeu, yNormNeu = myQuad.getUnifEdgePts(
numPtsU, numPtsV, [1, 0, 1, 1])
XbndNeu = np.concatenate((xPhysNeu, yPhysNeu, xNormNeu, yNormNeu),
axis=1).astype(data_type)
dwdx_neu, dwdy_neu = deriv_exact_sol(xPhysNeu, yPhysNeu)
def exact_sol(x,y):
u = np.sin(kx*np.pi*x)*np.sin(ky*np.pi*y)
return u
def deriv_exact_sol(x,y):
du = kx*np.pi*np.cos(kx*np.pi*x)*np.sin(ky*np.pi*y)
dv = ky*np.pi*np.sin(kx*np.pi*x)*np.cos(ky*np.pi*y)
return du, dv
#define the input and output data set
xmin = 0
xmax = 1
ymin = 0
ymax = 1
domainCorners = np.array([[xmin,ymin], [xmin,ymax], [xmax,ymin], [xmax,ymax]])
myQuad = Quadrilateral(domainCorners)
numPtsU = 28
numPtsV = 28
xPhys, yPhys = myQuad.getUnifIntPts(numPtsU, numPtsV, [0,0,0,0])
data_type = "float32"
Xint = np.concatenate((xPhys,yPhys),axis=1).astype(data_type)
Yint = rhs_fun(Xint[:,[0]], Xint[:,[1]])
xPhysBnd, yPhysBnd, _, _s = myQuad.getUnifEdgePts(numPtsU, numPtsV, [1,1,1,1])
Xbnd = np.concatenate((xPhysBnd, yPhysBnd), axis=1).astype(data_type)
Ybnd = exact_sol(Xbnd[:,[0]], Xbnd[:,[1]])
#define the model
tf.keras.backend.set_floatx(data_type)
(y_temp**2 - self.W**2 / 4))
v_left = -self.pei * (3 * self.nu * y_temp**2 * self.L)
u_val = xPhys * u_val + u_left
v_val = xPhys * v_val + v_left
return u_val, v_val
#define the input and output data set
beam_length = 8.
beam_width = 2.
pressure = 2.
domainCorners = np.array([[0., 0.], [0, beam_width], [beam_length, 0.],
[beam_length, beam_width]])
geomDomain = Quadrilateral(domainCorners)
model_data = dict()
model_data["E"] = 1e3
model_data["nu"] = 0.25
model_data["state"] = "plane stress"
numElemU = 20
numElemV = 10
numGauss = 4
#xPhys, yPhys = myQuad.getRandomIntPts(numPtsU*numPtsV)
xPhys, yPhys, Wint = geomDomain.getQuadIntPts(numElemU, numElemV, numGauss)
data_type = "float32"
Xint = np.concatenate((xPhys, yPhys), axis=1).astype(data_type)
Wint = np.array(Wint).astype(data_type)
u_left = self.pei * y_temp * ((2 + self.nu) *
(y_temp**2 - self.W**2 / 4))
v_left = -self.pei * (3 * self.nu * y_temp**2 * self.L)
u_val = xPhys * u_val + u_left
v_val = xPhys * v_val + v_left
return u_val, v_val
#define the input and output data set
beam_length = 8.
beam_width = 2.
domainCorners = np.array([[0., 0.], [0, beam_width], [beam_length, 0.],
[beam_length, beam_width]])
geomDomain = Quadrilateral(domainCorners)
numPtsU = 80
numPtsV = 40
#xPhys, yPhys = myQuad.getRandomIntPts(numPtsU*numPtsV)
xPhys, yPhys = geomDomain.getUnifIntPts(numPtsU, numPtsV, [0, 0, 0, 0])
data_type = "float32"
Xint = np.concatenate((xPhys, yPhys), axis=1).astype(data_type)
Yint = np.zeros_like(Xint).astype(data_type)
# prepare boundary points in the fromat Xbnd = [Xcoord, Ycoord, dir] and
# Ybnd = [trac], where Xcoord, Ycoord are the x and y coordinate of the point,
# dir=0 for the x-component of the traction and dir=1 for the y-component of
# the traction
if x<alpha*(t-1):
u[i] = 2*alpha/np.pi
v[i] = 0
elif x<=alpha*t:
u[i] = alpha/np.pi * (1-np.cos(np.pi*(t-x/alpha)))
v[i] = alpha/np.pi * np.pi * np.sin(np.pi*(t-x/alpha))
return u, v
#define the input and output data set
xmin = 0
xmax = 4
tmin = 0
tmax = 2
domainCorners = np.array([[xmin,tmin], [xmin,tmax], [xmax,tmin], [xmax,tmax]])
domainGeom = Quadrilateral(domainCorners)
numPtsU = 101
numPtsV = 101
xPhys, yPhys = domainGeom.getUnifIntPts(numPtsU,numPtsV,[0,0,0,0])
data_type = "float32"
Xint = np.concatenate((xPhys,yPhys),axis=1).astype(data_type)
Yint = np.zeros_like(xPhys).astype(data_type)
#boundary conditions at x=0
xPhysBnd, tPhysBnd, _, _ = domainGeom.getUnifEdgePts(numPtsU, numPtsV, [0,0,0,1])
Xbnd = np.concatenate((xPhysBnd, tPhysBnd), axis=1).astype(data_type)
Ybnd = np.where(tPhysBnd<=1, -np.sin(np.pi*tPhysBnd), 0).astype(data_type)
#initial conditions (displacement and velocity) for t=0
def deriv_exact_sol(x, y):
dudx = (1 - 2 * x) * (y - y**2)
dudy = (x - x**2) * (1 - 2 * y)
return dudx, dudy
#define the input and output data set
xmin = 0
xmax = 1
ymin = 0
ymax = 1
domainCorners = np.array([[xmin, ymin], [xmin, ymax], [xmax, ymin],
[xmax, ymax]])
myQuad = Quadrilateral(domainCorners)
numPtsU = 80
numPtsV = 80
numElemU = 20
numElemV = 20
numGauss = 4
boundary_weight = 1e4
xPhys, yPhys, Wint = myQuad.getQuadIntPts(numElemU, numElemV, numGauss)
data_type = "float32"
Xint = np.concatenate((xPhys, yPhys), axis=1).astype(data_type)
Wint = Wint.astype(data_type)
Yint = rhs_fun(Xint[:, [0]], Xint[:, [1]])