datastructures-functions-heat

Data structures and functions for heat equation

A skeleton code for these exercises are provided under this folder.

a) Create a two-dimensional 258x258 array of double precision numbers. Initialize the array such that the values are:

• 20.0 on the left boundary
• 85.0 on the upper boundary
• 70.0 on the right boundary
• 5.0 on the lower boundary

and otherwise zeros. A skeleton code is provided in 2d_array.c.

b) Write a double-for loop for evaluating the Laplacian using the finite-difference approximation:

As an input use the 258x258 array of Exercise a (or start from the skeleton laplacian.c. Evaluate the Laplacian only at the inner 256x256 points, the outer points are used as a boundary condition. As a grid spacing, use dx=dy=0.01. You can use the provided Makefile (use command make) for building the code.

c) Create a struct for a temperature field. The struct has the following elements:

• number of grid points nx and ny in the x- and y-direction
• the grid spacings dx and dy in the x- and y-direction
• the squares of grid spacings dx2 and dy2
• two dimensional array containing the data points of the field. The array contains also the boundary values, so its dimensions are nx+2 and ny+2.

d) Implement the initialization of the two dimensional array (exercise a) and finite-difference Laplacian (exercise b) in their own functions, which take as input the struct representing the temperature field (exercise 5c).