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Reproducing a Central Compact Finite-Difference Scheme for the Korteweg-de Vries Equation
An open-source Python reproduction of the TDCCS compact scheme for KdV by Salian, Samala and Ghosh, from coefficient derivation to all six examples.
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Optimization: Gradient, Newton and Quasi-Newton Methods and Minimum-Energy Trajectory Optimization
Gradient descent, Newton's method, and L-BFGS on convex logistic regression, followed by a minimum-energy trajectory solved by direct collocation and SLSQP.
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Computational Fluid Dynamics
A technical overview of CFD theory, numerical methods, a grid-convergence study, and a fully verified Python lid-driven cavity solver.
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Bayesian Inference for Inverse Problems: Metropolis Sampling for Source Identification and Linear Regression
Bayes' theorem, MAP estimation as ridge regression, and Metropolis sampling, applied to a synthetic wave-source inversion and the diabetes dataset.
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Domain Decomposition and Parallel Scaling for Wave Propagation: Amdahl, Gustafson and the Memory-Bandwidth Limit
Domain decomposition for a 2D wave equation under MPI, with Amdahl and Gustafson scaling and laptop benchmarks showing memory-bandwidth limits.