analytical#

analytical#

This module provides specific analytical solutions for basic problems where analytical solutions based on the continues form of PDE can be established. Usually, these problems are simpler and the analytical solution can be considered as an exact solution which can be used as a reference solution to evaluate and confirm other solutions ( e.g. numerical and neurical) before these solutions are used in more complex problems.

Analytical solutions are a problem specific and the list below shows the plan to work on these solutions in the future.

List of analytical solutions:

  • D1P1: 1-Dimension-1-Phase

  • D1P2: 1-Dimension-2-Phase (not available)

  • D1P3: 1-Dimension-3-Phase (not available)

  • D2P1: 2-Dimension-1-Phase (not available)

  • D2P2: 2-Dimension-2-Phase (not available)

  • D2P3: 2-Dimension-3-Phase (not available)

  • D3P1: 3-Dimension-1-Phase (not available)

  • D3P2: 3-Dimension-2-Phase (not available)

  • D3P3: 3-Dimension-3-Phase (not available)

Note

This list is rather a very optimistic one. For example, finding the analytical for a D3P3 might be impossible. However, constructing a solution based on simpler cases (e.g. D1P3) is a topic we would like to investigate.

Information:

  • design pattern: inheritance, abstraction

  • base class: Solution

  • base class type: ABS (abstract)

Classes

D1P1(model, sparse)

D1P1 solution class.

D1P2(**kwargs)

D1P2 solution class.

D1P3(**kwargs)

D1P3 solution class.

D2P1(**kwargs)

D2P1 solution class.

D2P2(**kwargs)

D2P2 solution class.

D2P3(**kwargs)

D2P3 solution class.

D3P1(**kwargs)

D3P1 solution class.

D3P2(**kwargs)

D3P2 solution class.

D3P3(**kwargs)

D3P3 solution class.

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