template<int dim, int n_rows, int n_columns, typename Number, typename Number2>
struct internal::EvaluatorTensorProduct< evaluate_evenodd, dim, n_rows, n_columns, Number, Number2 >
Internal evaluator for 1d-3d shape function using the tensor product form of the basis functions.
This class implements a different approach to the symmetric case for values, gradients, and Hessians also treated with the above functions: It is possible to reduce the cost per dimension from N^2 to N^2/2, where N is the number of 1D dofs (there are only N^2/2 different entries in the shape matrix, so this is plausible). The approach is based on the idea of applying the operator on the even and odd part of the input vectors separately, given that the shape functions evaluated on quadrature points are symmetric. This method is presented e.g. in the book "Implementing
Spectral Methods for Partial Differential Equations" by David A. Kopriva, Springer, 2009, section 3.5.3 (Even-Odd-Decomposition). Even though the experiments in the book say that the method is not efficient for N<20, it is more efficient in the context where the loop bounds are compile-time constants (templates).
- Template Parameters
-
| dim | Space dimension in which this class is applied |
| n_rows | Number of rows in the transformation matrix, which corresponds to the number of 1d shape functions in the usual tensor contraction setting |
| n_columns | Number of columns in the transformation matrix, which corresponds to the number of 1d shape functions in the usual tensor contraction setting |
| Number | Abstract number type for input and output arrays |
| Number2 | Abstract number type for coefficient arrays (defaults to same type as the input/output arrays); must implement operator* with Number and produce Number as an output to be a valid type |
Definition at line 1455 of file tensor_product_kernels.h.
template<int dim, int n_rows, int n_columns, typename Number , typename Number2 >
template<int direction, bool contract_over_rows, bool add, int type, bool one_line>
This function applies the tensor product kernel, corresponding to a multiplication of 1D stripes, along the given direction of the tensor data in the input array. This function allows the in and out arrays to alias for the case n_rows == n_columns, i.e., it is safe to perform the contraction in place where in and out point to the same address. For the case n_rows != n_columns, the output is only correct if one_line is set to true.
- Template Parameters
-
| direction | Direction that is evaluated |
| contract_over_rows | If true, the tensor contraction sums over the rows in the given shape_data array, otherwise it sums over the columns |
| add | If true, the result is added to the output vector, else the computed values overwrite the content in the output |
| type | Determines whether to use the symmetries appearing in shape values (type=0), shape gradients (type=1) or second derivatives (type=2, similar to type 0 but without two additional zero entries) |
| one_line | If true, the kernel is only applied along a single 1D stripe within a dim-dimensional tensor, not the full n_rows^dim points as in the false case. |
- Parameters
-
| shape_data | Transformation matrix with n_rows rows and n_columns columns, stored in row-major format |
| in | Pointer to the start of the input data vector |
| out | Pointer to the start of the output data vector |
Definition at line 1628 of file tensor_product_kernels.h.
1.8.11
