Problem Cache Module

Conceptual Overview

The ProblemCache class is a crucial internal component designed to optimize the performance of the MEEMEngine. Its purpose is to store pre-calculated components of the mathematical system to avoid redundant computations, especially when solving a problem over a range of frequencies.

Note

As an end-user of the OpenFLASH package, you will not need to interact with or create ProblemCache objects directly. The MEEMEngine automatically creates and manages a cache for each MEEMProblem instance it handles.

How it Works

When the MEEMEngine is initialized with a problem, it builds a ProblemCache that:

  1. Analyzes the System: It identifies which parts of the governing matrices (A) and vectors (b) are constant (frequency-independent) and which parts change with the wave frequency.

  2. Pre-computes Templates: It calculates the frequency-independent parts once and stores them in “template” matrices.

  3. Stores Calculation Logic: For the frequency-dependent parts, it stores lightweight functions (closures) that can be quickly executed to calculate the values for any given frequency.

When a user requests a solution at a new frequency, the engine simply copies the pre-computed templates and runs the stored functions to fill in the missing pieces, rather than re-building the entire system from scratch. This caching strategy is the key to the engine’s efficiency during frequency sweeps.