Factorization in block-triangularly implicit methods for shallow water applications

Diagonally implicit Runge-Kutta methods for 3D shallow water applications

We construct A-stable and L-stable diagonally implicit Runge-Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge-Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge-Kutta methods are suitable methods for integrating shallow water problems in the sense that the stab...

Triangularly Implicit Iteration Methods for ODE-IVP Solvers

It often happens that iteration processes used for solving the implicit relations arising in ODE-IVP methods only start to converge rapidly after a certain number of iterations. Fast convergence right from the beginning is particularly important if we want to use so-called step-parallel iteration in which the iteration method is concurrently applied at a number of step points. In this paper, we...

Block Implicit One - Step Methods

A class of one-step methods which obtain a block of r new values at each step are studied. The asymptotic behavior of both implicit and predictor-corrector procedures is examined.

Context-aware factorization methods for implicit feedback based recommendation problems

Shallow Water Laser Bathymetry: Accomplishments and Applications

Airbome Laser Bathymetry (ALB) is a technique primarily aimed at augmenting nautical chart production and bathymetric mapping capability in relatively shallow coastal waters. The potential of waterpenetrating airborne laser radar to provide cost effective characterization of underwater topography to depths as great as 50 meters, depending on water clarity, has triggered a number of research and...