Mathematical & Computational Physics
5 terms
Parallel Computing
Mathematical & Computational Physics
Speedup Factor S(P)
A computational architecture where large physical calculations are divided into smaller sub-tasks executed simultaneously across multiple processor cores or GPUs.
Amdahl's Law Speedup S(P) = 1 / ((1 - p) + p / P)
Partial Differential Equations
Mathematical & Computational Physics
Multivariable Differential Equations
Differential equations containing unknown multivariable functions and their partial derivatives with respect to multiple independent variables.
Elliptic (Laplace), Parabolic (Heat), Hyperbolic (Wave)
Perturbation Theory
Mathematical & Computational Physics
Approximation Power Series
A set of mathematical approximation methods for finding an approximate solution to a complex problem by starting from the exact solution of a simpler unperturbed problem.
H = H₀ + λ H', E_n = E_n^(0) + λ E_n^(1) + λ² E_n^(2) + ...
Physical Simulation
Mathematical & Computational Physics
Computational Modeling
The use of computer programs and numerical algorithms to simulate the time-dependent physical behavior of real-world or theoretical systems.
x(t + Δt) = x(t) + v(t) Δt + ½ a(t) Δt²
Poisson Brackets
Mathematical & Computational Physics
Phase Space Operation
An algebraic operation between two phase space functions describing time evolution and conservation laws in Hamiltonian mechanics.
{f, g} = ∑ ((∂f / ∂q_i)(∂g / ∂p_i) - (∂f / ∂p_i)(∂g / ∂q_i))