def laplace2(self, weight=1):
"""
Generates a symbolic expression for the double Laplacian
wrt. all spatial dimensions.
"""
order = self.space_order/2
first = sum([second_derivative(self, dim=d, order=order)
for d in self.space_dimensions])
return sum([second_derivative(first * weight, dim=d, order=order)
for d in self.space_dimensions])
def laplace2(self, weight=1):
"""Symbol for the double laplacian wrt all spatial dimensions"""
order = self.space_order/2 + self.space_order/2 % 2
first = sum([second_derivative(self, dim=d,
order=order)
for d in self.indices[1:]])
second = sum([second_derivative(first * weight, dim=d,
order=order)
for d in self.indices[1:]])
return second
def dy2z2(self):
"""Symbol for the second cross derivative wrt the y,z dimension"""
return second_derivative(self.dy2, dim=z, order=self.space_order)
def dx2y2(self):
"""Symbol for the second cross derivative wrt the x,y dimension"""
return second_derivative(self.dx2, dim=y, order=self.space_order)