DenseMathOpsMixin

class grids.mixins.mathops.DenseMathOpsMixin

Mixin class for dense differential geometry operations on structured grids.

This class provides high-level numerical implementations of common differential geometry operators—such as gradients, divergence, and Laplacians—on fields defined over structured grids with curvilinear coordinate systems.

It serves as a convenience interface to the low-level functions in differential_geometry, managing:

• Axis labeling and broadcasting between tensor fields and grid domains.

• Automatic handling of coordinate expressions like metric tensors and volume terms.

• Support for lazy-loading or memory-intensive buffers through optional chunked execution.

• Compatibility with ghost zones and progress bars.

Methods

__init__()
compute_function_on_grid(func, /[, ...])	Evaluate a coordinate-based function over the grid domain.
dense_adjust_tensor_signature(tensor_field, ...)	Adjust the index signature of a tensor field by raising or lowering multiple indices.
dense_contract_with_metric(tensor_field, ...)	Contract a tensor index with the metric tensor or its inverse.
dense_contravariant_gradient(tensor_field, ...)	Compute the contravariant gradient of a dense-representation tensor field on a grid.
dense_covariant_gradient(tensor_field, ...)	Compute the covariant gradient of a dense-representation tensor field on a grid.
dense_element_wise_laplacian(field, ...[, ...])	Compute the element-wise Laplacian of an array-valued field on the grid.
dense_element_wise_partial_derivatives(...)	Compute the element-wise partial derivatives of an array-valued field over the grid.
dense_gradient(tensor_field, field_axes, /)	Compute the element-wise gradient of a tensor field over a grid.
dense_lower_index(tensor_field, field_axes, ...)	Lower a single contravariant index of a tensor field.
dense_raise_index(tensor_field, field_axes, ...)	Raise a single covariant index of a tensor field.
dense_scalar_laplacian(field, field_axes, /)	Compute the element-wise Laplacian of a tensor field.
dense_vector_divergence(vector_field, ...[, ...])	Compute the divergence of a vector field, with automatic basis dispatching.
dense_vector_divergence_contravariant(...[, ...])	Compute the divergence of a contravariant vector field on a grid.
dense_vector_divergence_covariant(...[, ...])	Compute the divergence of a covariant vector field on a grid.