pymor.analyticalproblems.thermalblock

Module Contents

Functions

thermal_block_problem

Analytical description of a 2D 'thermal block' diffusion problem.

pymor.analyticalproblems.thermalblock.thermal_block_problem(num_blocks=(3, 3), parameter_range=(0.1, 1))

Analytical description of a 2D ‘thermal block’ diffusion problem.

The problem is to solve the elliptic equation

- ∇ ⋅ [ d(x, μ) ∇ u(x, μ) ] = 1

on the domain [0,1]^2 with Dirichlet zero boundary values. The domain is partitioned into nx x ny blocks and the diffusion function d(x, μ) is constant on each such block i with value μ_i.

----------------------------
|        |        |        |
|  μ_4   |  μ_5   |  μ_6   |
|        |        |        |
|---------------------------
|        |        |        |
|  μ_1   |  μ_2   |  μ_3   |
|        |        |        |
----------------------------

Parameters

num_blocks

The tuple (nx, ny)

parameter_range

A tuple (μ_min, μ_max). Each Parameter component μ_i is allowed to lie in the interval [μ_min, μ_max].