spectral_galerkin_heat.physics.spectral_cpu_kernels
===================================================

.. py:module:: spectral_galerkin_heat.physics.spectral_cpu_kernels

.. autoapi-nested-parse::

   CPU-based spectral method kernels for the heat equation.

   Public functions in this module are called by SpectralSolver (NumpyBackend):
   - ``update_modes_etd1``: Time integration step
   - ``compute_latent_heat_source``: Latent heat and evaporation effects
   - ``reconstruct_surface_temperature``: Extract solution on top surface



Classes
-------

.. autoapisummary::

   spectral_galerkin_heat.physics.spectral_cpu_kernels.SpectralSolverState


Functions
---------

.. autoapisummary::

   spectral_galerkin_heat.physics.spectral_cpu_kernels.update_modes_etd1
   spectral_galerkin_heat.physics.spectral_cpu_kernels.add_source_term_modes
   spectral_galerkin_heat.physics.spectral_cpu_kernels.add_bottom_surface_source


Module Contents
---------------

.. py:class:: SpectralSolverState(phys, geom, num, fine)

   Bases: :py:obj:`spectral_galerkin_heat.physics.spectral_state.SpectralSolverState`


   CPU spectral state: :class:`spectral_state.SpectralSolverState` bound to NumPy.


.. py:function:: update_modes_etd1(aK, KK, Cp_broadcast, B_scaled, a_temp_out)

   Update spectral coefficients for ETD1 scheme.
   Calculates: a_out = aK + (KK * Cp) * B_scaled


.. py:function:: add_source_term_modes(a_temp, KK, Q_modes)

   Accumulate volumetric source term into temperature modes.
   a_temp += KK * Q_modes


.. py:function:: add_bottom_surface_source(a_temp, KK, Cp_broadcast_bottom, B_scaled)

   Accumulate a surface source at z=0 into temperature modes.
   a_temp[p,:,:] += KK[p,:,:] * Cp_bottom[p] * B_scaled[:,:]