diff --git a/README.md b/README.md
index 845e672..feabad2 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
# HIVE: Heating by Induction to Verify Extremes
-_Nuno Nobre and Karthikeyan Chockalingam_
+_Nuno Nobre, Josh Williams and Karthikeyan Chockalingam_
###
@@ -73,11 +73,12 @@ proceeds as follows:
Solved for the magnetic vector potential $\mathbf{A} \in \mathcal{N}^0_I$
[(*)](https://defelement.com/elements/examples/tetrahedron-nedelec1-lagrange-1.html),
- everywhere in space and for each time step, with Dirichlet boundary
- conditions on the $\mathbf{n}$-oriented plane boundary of the vacuum
- chamber where the coil terminals sit, $\mathbf{A} × \mathbf{n} = 0$, and
- Neumann boundary conditions on its remaining $\mathbf{n}$-oriented outer
- surfaces, $\mathbf{∇} × \mathbf{A} × \mathbf{n} = 0$.
+ everywhere in space and for each time step $\Delta t_\mathrm{EM}$ of only a
+ reduced selection of cycles of the voltage source in (1), with Dirichlet
+ boundary conditions on the $\mathbf{n}$-oriented plane boundary of the
+ vacuum chamber where the coil terminals sit, $\mathbf{A} × \mathbf{n} = 0$,
+ and Neumann boundary conditions on its remaining $\mathbf{n}$-oriented
+ outer surfaces, $\mathbf{∇} × \mathbf{A} × \mathbf{n} = 0$.
$ν$ is the magnetic reluctivity (the reciprocal of the magnetic
permeability) and $σ$ is the electrical conductivity.
The right-hand side is non-zero only within the coil, see (1), and is
@@ -88,14 +89,17 @@ proceeds as follows:
Solved for the temperature $T \in \mathcal{P}^1$
[(*)](https://defelement.com/elements/examples/tetrahedron-lagrange-equispaced-1.html),
- everywhere in space and for each time step, with Neumann boundary conditions
- on the $\mathbf{n}$-oriented outer surface of the vacuum chamber,
- $\mathbf{∇}T \cdot \mathbf{n} = 0$, and initial conditions everywhere in
- space, $T = T_\mathrm{room}$.
+ everywhere in space and for each time step $\Delta t_\mathrm{HT}$, with
+ Neumann boundary conditions on the $\mathbf{n}$-oriented outer surface of
+ the vacuum chamber, $\mathbf{∇}T \cdot \mathbf{n} = 0$, and initial
+ conditions everywhere in space, $T = T_\mathrm{room}$.
$ρ$ is the density, $c$ is the specific heat capacity, and $k$ is the
thermal conductivity.
- The right-hand side is the Joule heating term which, as of this writing, we
- compute only on the target.
+ The right-hand side is the Joule heating term which we compute only on the
+ target and is time-averaged over the simulated time interval in (2). This
+ enables quicker simulations by solving for the temperature $T$ on a larger
+ time scale than the magnetic vector potential $\mathbf{A}$, i.e.
+ $\Delta t_\mathrm{HT} >> \Delta t_\mathrm{EM}$.
See [input/Parameters.i](input/Parameters.i) for the set of parameters
influencing the simulation.
@@ -124,11 +128,6 @@ accuracy, time-to-solution and general usability.
### Time-to-solution
-* Switch to a time-averaged Joule heating source in the heat equation sub-app
- to keep the problem tractable when simulating over a long physical time span.
- The $\mathbf{A}$ formulation sub-app will then sub-cycle, i.e. perform
- multiple time steps for each time step of the heat equation sub-app.
-
* Study the potential gains of solving all, but most importantly the
$\mathbf{A}$ formulation sub-app, on the GPU simply via PETSc/hypre flags.