Numerical Analysis
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Boundary Integral Methods
2 mins
Numerical Analysis
Optics
Quantum Mechanics
Simulation
Essentially, a Boundary Integral Method (BIM) reduces the degrees of freedom of a problem to those of the boundary. It also means that the problem becomes meshless, which means that there is no need for simple domains.
State Equation Based Simulation
3 mins
Numerical Analysis
Fluids
Elastic Solids
Simulation
There is a technique called Smoothed Particle Hydrodynamics ( SPH) which deals with simulating the behaviour of continuous media such as fluids, deformable solids, and viscous materials. It is a type of phenomenological simulation, as it consists of heuristic arguments rather than physical principles.
Fiber optics and non-linearity
2 mins
Numerical Analysis
Optics
Nonlinear
Simulation
Fiber optics technology has revolutionized communication by enabling the efficient transmission of data over long distances. At the heart of this technology lies the Nonlinear Schrödinger Equation (NLSE), a mathematical model that describes the behavior of optical pulses in fiber optic communication systems.
Wave Simulations
1 min
Numerical Analysis
Electrodynamics
Acoustics
Simulation
Wave simulations are essential in optics and electrodynamics. Here are some of the simulations I’ve done for wave propagation using finite-difference schemes.
The difference between using ABCs and not using these are highlighted in Figures 1 and 2.
Simulated Annealing
1 min
Numerical Analysis
Stochastics
Simulation
Similar to the Ising Model, Simulated Annealing takes a step implements a similar cost function to that of the Ising Hamiltonian. Once again, the probability of accepting a less-efficient state follows the Maxwell-Boltzmann distribution.
Ising model
2 mins
Numerical Analysis
Statistical Mechanics
Stochastics
Simulation
The Metropolis-Hastings algorithm for simulating the Lenz-Ising model is an excellent example of a Markov chain, since the former is actually a version of a Markov chain Monte Carlo (MCMC) simulation.