# Reduced Basis

We are interested on applying the reduced basis method to the heat equation for the 3D benchmark. \rho c \partial_t T - k \Delta T = f(x,t,v) The parameter of interest is $v$, the velocity of the torch. The output of interest is the mean temperature at each time.

To mimic the torch, we will use the Goldak function.

## Offline operations

• Construct an EIM approximation of $f(x,t,v)$ such that f_M(x,t,v) \approx \sum_{i=1}^M g_M(t,v)\xi(x)

• Construct the reduced basis

## Oneline operations

• Evaluate the output