In this chapter, we present several significant improvements to the original numerical implementation of the two-dimensional method introduced in [13], as described in the previous chapter. The numerical solution of the associated approximate integral equation (2.3) consists of two main parts: efficient, high-order numerical quadrature rules and an efficient linear solver. The numerical evaluat...

Numerical weather predicting models often require solving a 3-D Helmholtz problem which derived from the governing equation of dynamical core in Met Office Unified Model, by preconditioned iterative solvers. In this dissertation, a GPU implementation of preconditioned conjugate gradient (CG) iterative method will be focused on. A given serial code has been ported on GPU. According to the portin...

Numerical implementation of generalized Coddington equations for ophthalmic lens design P. Rojo, S. Royo, J. Ramírez & I. Madariaga a UPC-CD6, Center for Sensor, Instruments and Systems Development, Universitat Politècnica de Catalunya, Rambla Sant Nebridi 10 Terrassa E08222, Spain b Vallès Oftalmologia Recerca VO-R. Hospital General de Catalunya. 4th floor Green building, Room 387. C/Pedro I P...

In this paper, we describe our experience in writing parallel numerical algorithms using Hierarchically Tiled Arrays (HTAs). HTAs are classes of objects that encapsulate parallelism. HTAs allow the construction of single-threaded parallel programs where a master process distributes tasks to be executed by a collection of servers holding the components (tiles) of the HTAs. The tiled and recursiv...

In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on initial conditions is explicit and the equations governing the orientation of the body involve only real numbers. Based on these results, an efficient method...

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinementbased discretizations of elliptic equations, they tend to be less effective for algebraic systems which arise from discretizations on locally refined meshe...

Fourier ptychography (FP) utilizes illumination control and computational post-processing to increase the resolution of bright-field microscopes. In effect, FP extends the fixed numerical aperture (NA) of an objective lens to form a larger synthetic system NA. Here, we build an FP microscope (FPM) using a 40X 0.75NA objective lens to synthesize a system NA of 1.45. This system achieved a two-sl...

In this paper we present our experience with the solution how to make the implementation of 3D Delaunay triangulation more stable. A brief overview of possible methods is given. The proper solution is found in geometric predicates. Tests of two different implementations of them are provided and results of incorporating one of them into our implementation of 3D Delaunay triangulator are presente...

This paper presents an efficient implementation of two large numerical simulations using a parallel programming environment called Athapascan. This library eases parallel implementations by managing communications and synchronisations. It provides facilities to adapt the schedule to efficiently map the application on the target architecture.

The Einstein-Brillouin-Keller EBK quantization equation is used to determine the energy levels of a two-body system with an arbitrary central potential that allows for bound states. The treatment is based on the conservation laws and avoids both the Newtonian and Schrödinger differential equations. Because analytic solutions for the energy levels do not exist in general, the EBK condition is ap...