By Timo Betcke
© Copyright 2020.
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Assignment 3 – Sparse
matrix formats on GPUs
Assignment 4 – Time-dependent problems
Submission Deadline: We 15 December, 10am
Consider a square plate with sides . At time t = 0 we are heating
the plate up such that the temperature is on one side and on the other
sides. The temperature evolves according to . At what time does the
plate reach at the center of the plate? Implement a finite difference scheme
and try with explicit and implicit time-stepping. By increasing the number of
discretisation points demonstrate how many correct digits you can achieve. Also,
plot the convergence of your computed time against the actual time. To 12 digits
the wanted solution is .
A GPU implementation of the explicit time-stepping scheme is not necessary but
would be expected for a very high mark beyond 80%.
[−1, 1]×[−1, 1]
u = 5 u = 0
ut = Δu t
∗
u = 1
t
∗
t
∗ = 0.424011387033
https://tbetcke.github.io/hpc_lecture_notes/assignment_3.html