def setupPDE_vector_calculus(gridSize, equation):
pde = PDE(gridSize, gridSize)
pde.setEquationExpression(PDEExpressionType.VECTOR_CALCULUS, equation)
pde.setVectorVariable("r", dimension=2)
pde.configureGrid()
return pde
def setupPDE_vector_calculus():
# 3. Equation as vector calculus without aux function eps
pde = PDE(64.0, 64.0)
pde.setEquationExpression(PDEExpressionType.VECTOR_CALCULUS,
"div(grad( u(r) ))")
pde.setVectorVariable("r", dimension=2)
pde.configureGrid()
return pde
def setupPDE_vector_calculus_with_eps():
# 4. Equation as vector calculus with aux function eps
pde = PDE(64.0, 64.0)
pde.setEquationExpression(PDEExpressionType.VECTOR_CALCULUS,
"div(eps(r) * grad( u(r) ))")
pde.setVectorVariable("r", dimension=2)
pde.setAuxiliaryFunctions({'eps': eps})
pde.configureGrid()
return pde
def setupPDE_finite_differences_with_eps():
# 2. Finite Differences with aux function eps
pde = PDE(64.0, 64.0)
pde.setEquationExpression(PDEExpressionType.FINITE_DIFFERENCES,
'eps(i+1/2,j)*(u(i+1,j)-u(i,j)) - eps(i-1/2,j)*(u(i,j)-u(i-1,j)) + ' + \
'eps(i,j+1/2)*(u(i,j+1)-u(i,j)) - eps(i,j-1/2)*(u(i,j)-u(i,j-1))')
pde.setAuxiliaryFunctions({'eps': eps})
pde.configureGrid()
return pde
def setupPDE_finite_differences():
# 1. Finite Differences without aux function eps
pde = PDE(64.0, 64.0)
pde.setEquationExpression(
PDEExpressionType.FINITE_DIFFERENCES,
'(u(i+1,j)-u(i,j)) - (u(i,j)-u(i-1,j)) + (u(i,j+1)-u(i,j)) - (u(i,j)-u(i,j-1))'
)
pde.configureGrid()
return pde