Computational Science Masterclass
Build advanced physics simulations using finite element methods, differential equations, and numerical analysis with Fortran.
Finite Element Methods
Implement structural mechanics and heat transfer simulations using FEM.
Computational Fluid Dynamics
Model fluid dynamics with finite-difference methods and Navier-Stokes equations.
Parallel Algorithms
Accelerate large-scale simulations using OpenMP and MPI.
Course Syllabus
Core Theoretical Concepts
- 📦 PDE discretization techniques
- 🧮 Mesh generation and adaptive refinement
- 📊 Stability and convergence analysis
Practical Implementation
- 🔬 Heat equation solver with implicit time stepping
- 🌊 Navier-Stokes simulations using FV methods
- 🧬 Multigrid acceleration for elliptic problems
Masterclass Projects
Structural Dynamics Simulator
Analyze stress distribution in buildings under seismic loading.
View Details →Climate System Model
Simulate atmospheric circulation patterns with finite volume methods.
View Details →Quantum Monte Carlo
Calculate ground state energies using variational quantum Monte Carlo methods.
View Details →Sample Implementation
! Finite difference solver for Poisson equation
program poisson_solver
implicit none
integer, parameter :: N = 100
real(8) :: u(N,N), rhs(N,N)
integer :: i, j
! Initialize RHS and BC
do i = 1, N
do j = 1, N
rhs(i,j) = 0.0d0
if (i == 1 .or. i == N .or. j == 1 .or. j == N) then
u(i,j) = 100.0d0 ! Dirichlet BC
else
u(i,j) = 100.0d0 ! Initial guess
end if
end do
end do
! Solve using SOR method
call sor_solver(u, rhs, 0.6)
contains
subroutine sor_solver(u, rhs, omega)
real(8), intent(inout) :: u(:, :)
real(8), intent(in) :: rhs(:, :)
real(8), intent(in) :: omega
integer :: max_iter
integer :: iter
do iter = 1, max_iter
do i = 2, N-1
do j = 2, N-1
u(i,j) = (rhs(i,j) + u(i-1,j) + u(i+1,j) + u(i,j-1) + u(i,j+1)) * omega / 4
end do
end do
end do
end subroutine sor_solver
end program poisson_solver