def create_finite_differences_configuration():
gridConfig = GridConfiguration()
gridConfig.add(ConstantGridValueProvider(1.0), 1, 0)
gridConfig.add(ConstantGridValueProvider(1.0), -1, 0)
gridConfig.add(ConstantGridValueProvider(1.0), 0, 1)
gridConfig.add(ConstantGridValueProvider(1.0), 0, -1)
gridConfig.add(ConstantGridValueProvider(-4.0), 0, 0)
return gridConfig
def makeStandardPDEConfig():
# this encodes the linearized PDE: -4u(i,j)+u(i+1,j)+u(i-1,j)+u(i,j+1)+u(i,j-1) = -rho(i,j)
# (u(i+1,j)-u(i,j))/deltaX - (u(i,j)-u(i-1,j))/deltaX +
# (u(i,j+1)-u(i,j))/deltaY - (u(i,j)-u(i,j-1))/deltaX =
# -rho(i,j)
#
# u(i+1,j)-u(i,j) - (u(i,j)-u(i-1,j)) + ... (i<->j) = -rho(i,j)
gridConfig = GridConfiguration()
gridConfig.add(ConstantGridValueProvider(1.0), 1, 0)
gridConfig.add(ConstantGridValueProvider(1.0), -1, 0)
gridConfig.add(ConstantGridValueProvider(1.0), 0, 1)
gridConfig.add(ConstantGridValueProvider(1.0), 0, -1)
gridConfig.add(ConstantGridValueProvider(-4.0), 0, 0)
return gridConfig
def make_grid_config(self, eps):
gridConfig = GridConfiguration()
for functionCall in self.values:
if type(functionCall.prefactorExpr) is NumberExpression:
gridConfig.add(
ConstantGridValueProvider(
functionCall.prefactorExpr.value),
int(functionCall.offset.x), int(functionCall.offset.y))
else:
gridConfig.add(
FunctionGridValueProvider(functionCall.makeFunction(eps)),
int(functionCall.offset.x), int(functionCall.offset.y))
return gridConfig
def make_finite_differences_poisson_equation_in_matter(eps):
gridConfig = GridConfiguration()
gridConfig.add(
FunctionGridValueProvider((lambda i, j: 0.5 *
(eps(i, j) + eps(i + 1, j)))), 1, 0)
gridConfig.add(
FunctionGridValueProvider((lambda i, j: 0.5 *
(eps(i, j) + eps(i - 1, j)))), -1, 0)
gridConfig.add(
FunctionGridValueProvider((lambda i, j: 0.5 *
(eps(i, j) + eps(i, j + 1)))), 0, 1)
gridConfig.add(
FunctionGridValueProvider((lambda i, j: 0.5 *
(eps(i, j) + eps(i, j - 1)))), 0, -1)
gridConfig.add(
FunctionGridValueProvider((lambda i, j: -0.5 * (4 * eps(i, j) + eps(
i + 1, j) + eps(i - 1, j) + eps(i, j + 1) + eps(i, j - 1)))), 0, 0)
return gridConfig
if __name__ == '__main__':
np.set_printoptions(threshold=np.nan)
delta = 1.0
rect = Rectangle(0, 0, 3.0, 3.0)
g = Geometry(rect, delta)
boundaryCondition = RectangularBoundaryCondition(g)
charges = make_central_charge(g)
gridConfig = GridConfiguration()
gridConfig.add(ConstantGridValueProvider(-4.0), 0,0)
gridConfig.add(ConstantGridValueProvider(1.0), 1, 0)
gridConfig.add(ConstantGridValueProvider(1.0), -1, 0)
gridConfig.add(ConstantGridValueProvider(1.0), 0, 1)
gridConfig.add(ConstantGridValueProvider(1.0), 0, -1)
fdm = FiniteDifferencesMethod3(g, boundaryCondition, gridConfig, charges)
fdm.solve()
fdm.printMatrix()
#f = (lambda i, j:
# -0.5 * 2 * eps(i,j))