Jacobi_Iterative_With_Mutex

A multi-threaded program that computes the heat distribution problem based on the Jacobi iterative method.

Environment: Linux

Heat Distribution Problem

The heat distribution problem is an important study in science/engineering and plays a key role in climate modeling and weather forecasting. The two-dimensional (2D) heat distribution problem is to find the steady state temperature distribution within an area which has known fixed temperatures along each of its edges.

Jacobi Iterative Method

The above equation is essentially the Gauss-Seidel iterative method which relies on a sequential order of computation and is thus more difficult to parallelize. In this assignment, we adopt the Jacobi iterative method:

𝑤[𝑖,𝑗] = (𝑢[𝑖 − 1,𝑗] + 𝑢[𝑖 + 1,𝑗] + 𝑢[𝑖,𝑗 − 1] + 𝑢[𝑖, 𝑗 + 1]) / 4

In the Jacobi method, we use two 2D arrays to store the temperature distribution. The array w stores the current iteration’s solution while the array u stores the previous iteration’s solution. For each iteration, we calculate the temperature value of a point by computing the average temperature value of its four neighbors obtained from the previous iteration.

Use multithreading and synchronization to improve the calculation effiency

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To run the code:

Use the default setings: rows = 200, columns = 200, threads = 2

./jacobi_cond

Use other parameters: e.g., rows = 400, columns = 400, threads = 8

./jacobi_cond 400 400 8