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.