If I have the solution to my PDE, what is the best method to get it's derivative?

dokken · July 20, 2023, 11:13am

In legacy dolfin:
Project the gradient into a suitable space and use point evaluation.
See:

In Dolfinx you can use the Expression class.

FEniCS/dolfinx/blob/81681dc1cb1743a98661162e12f34f4d887d2442/python/dolfinx/fem/function.py#L175


      
                      return _cpp.fem.create_expression_complex64
                  elif dtype is np.complex128:
                      return _cpp.fem.create_expression_complex128
                  else:
                      raise NotImplementedError(f"Type {dtype} not supported.")
          
              ffi = module.ffi
              self._cpp_object = create_expression(dtype)(ffi.cast("uintptr_t", ffi.addressof(self._ufcx_expression)),
                                                          coeffs, constants, mesh, self.argument_function_space)
          
          def eval(self, cells: np.ndarray, values: typing.Optional[np.ndarray] = None) -> np.ndarray:
              """Evaluate Expression in cells. Values should have shape
              (cells.shape[0], num_points * value_size * num_all_argument_dofs).
              If values is not passed then a new array will be allocated.
          
              """
              _cells = np.asarray(cells, dtype=np.int32)
              if self.argument_function_space is None:
                  argument_space_dimension = 1
              else:
                  argument_space_dimension = self.argument_function_space.element.space_dimension

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If I have the solution to my PDE, what is the best method to get it's derivative?

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