Heat Equation Solver

Problem Statement

The heat equation is a partial differential equation that describes the propagation of heat in a region over time. The aim of our project is to develop and implement a parallelized simulation of heat diffusion using the explicit finite difference method on a three-dimensional grid.

$\frac{∂U}{∂t}$ = $a (\frac{∂^2U}{∂x^2}$ + $\frac{∂^2U}{∂y^2}$ + $\frac{∂^2U}{∂z^2}$)

Where $x$, $y$ and $z$ are spatial variables, $t$ is the time. $U$ is the temperature, $a$ is the thermal conductivity which differs between materials, it will be used as a diffusion constant.

For this problem we will specify the intial condition $U(x, y, z, t)$ at $t=0.$ As it is not possible to simulate the problem over infinite spatial domain (where $x∈(−∞,+∞)$, $y∈(−∞,+∞)$ and $z∈(−∞,+∞)$ ), we specify boundary confitions for the region.

Test serial code

Type in your terminal to compile :
g++ heat3D_Serial.cpp -o heat3D_Serial.out

To Run :
./heat3D_Serial.out

Test OpenMP code(Modify number of threads using omp_set_num_threads() as required)

Type in your terminal to compile :
g++ -fopenmp heat3D_OpenMP.cpp -o heat3D_OpenMP.out

To Run :
./heat3D_OpenMP.out

Test CUDA code

Type in your terminal to compile :
nvcc heat3D_CUDA.cu -o heat3D_CUDA.out

To Run :
./heat3D_CUDA.out