In the last lecture, we were introduced to the Interior Point Method. The simplex method solves linear programming problems (LP) by visiting extreme points (vertices) on the boundary of the feasible set. In contrast, the interior point method is based on algorithms that find an optimal solution while moving in the interior of the feasible set. Intuitively, in each iteration of the interior poin...

Boundary layer turbulence in coastal regions differs from that deep ocean because of bottom interactions. In this paper, we focus on the merging surface and boundary layers a finite-depth by numerically solving wave-averaged equations using large eddy simulation method. The fluid is driven combined effects wind stress, wave, steady current presence stable vertical stratification. resulting flow...

The effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. The governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. The obtained ordinarydifferential equations ar...

Maxwell’s equations are considered with transparent boundary conditions, with initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The proposed computational scheme only involves the interior domain and its boundary. The transparent boundary conditions are imposed via a time-dependent boundary integ...

A simple model of the thermohaline circulation (THC) is formulated, with the objective to represent explicitly the geostrophic force balance of the basinwide THC. The model comprises advective-diffusive density balances in two meridional-vertical planes located at the eastern and the western walls of a hemispheric sector basin. Boundary mixing constrains vertical motion to lateral boundary laye...

Given a sheet of paper and a prescribed folding of its boundary, is there a way to fold the paper’s interior without stretching so that the boundary lines up with the prescribed boundary folding? For polygonal boundaries nonexpansively folded at finitely many points, we prove that a consistent isometric mapping of the polygon interior always exists and is computable in polynomial time.

In this paper we review our recent work on mathematical analysis and efficient numerical computation for the semiclassical limits of the ground and excited states of the Gross-Pitaevskii equation (GPE) with applications in Bose-Einstein condensation and nonlinear optics. We begin with the timeindependent GPE and show how to reformulate it into a singularly perturbed nonlinear eigenvalue problem...

the effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. the governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. the obtained ordinarydifferential equations ar...