Geometric Numerical Integration Research Papers (original) (raw)

A new algorithm is proposed for triangular mesh reconstruction from 3D scattered points based on the existing intrinsic property driven (IPD) method. The improvements include a new approach to determine the seed triangle, a new approach... more

A new algorithm is proposed for triangular mesh reconstruction from 3D scattered points based on the existing intrinsic property driven (IPD) method. The improvements include a new approach to determine the seed triangle, a new approach to define the influence region for active edge, and a new approach to select the best active point. The new triangle is also tested with the constraint of geometric integrity. Our algorithm has been tested on some unorganized 3D point clouds. From the experimental results it can be found that our approach has the ability to generate more accurate details in the recovered surfaces.

Information available from ephemeris data, combined with a few ground control points, is used to carry out the geometric combination of NOAA, AVHRR, and SPOT images by means of orbital models for each satellite. The observation conditions... more

Information available from ephemeris data, combined with a few ground control points, is used to carry out the geometric combination of NOAA, AVHRR, and SPOT images by means of orbital models for each satellite. The observation conditions are reconstructed and the areas observed in common determined in the SPOT image pixels and each low-resolution AVHRR pixel. The determination of effective

This paper surveys some of the fundamental properties of symplectic integration schemes for classical mechanics and particle methods in particular. The widely used Störmer-Verlet method is discussed in detail and implications of... more

This paper surveys some of the fundamental properties of symplectic integration schemes for classical mechanics and particle methods in particular. The widely used Störmer-Verlet method is discussed in detail and implications of conservation of symplecticity on long term simulations are outlined. The second part of the paper describes the application of a Lagrangian particle method and the Störmer-Verlet time integrator to numerical weather prediction (NWP). A simple vertical slice model and non-hydrostatic flow over orography are discussed in detail.

Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation. Using the method of lines,... more

Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation. Using the method of lines, the discretizations are constructed by applying Castillo-Grone's mimetic operators in the space direction and explicit trapezoidal integrator in the time direction. Convergence tests and conservation property of the schemes are presented. Computed profiles capture both the saturation overshoot and pressure overshoot phenomena. Comparisons between numerical results and experiments illustrate the effectiveness and different features of the models. Keywords Castillo-Grone's mimetic operators · saturation overshoot · pressure overshoot · dynamic capillary pressure · rate independent hysteresis

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrödinger-KdV equations (CSKE) with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral (MSFP) scheme for the... more

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrödinger-KdV equations (CSKE) with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral (MSFP) scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank–Nicholson (CN) method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.

In this work we present a mathematical formulation for geometric modelling which may be applied in spaces of any dimension. The model can be seen as an example of a graphic object algebra [see Torres, J. C. and Clares, B., Graphics... more

In this work we present a mathematical formulation for geometric modelling which may be applied in spaces of any dimension. The model can be seen as an example of a graphic object algebra [see Torres, J. C. and Clares, B., Graphics objects: a mathematical abstract model for computer graphics. Computer Graphics Forum, 1993, 12(5), 311–328 and Feito, F. R. and

We apply Munthe-Kaas and Crouch–Grossman methods in the solution of some mechanical problems. These methods are quite new, and they exploit intrinsic properties of the manifolds defined by the mechanical problems, thus ensuring that the... more

We apply Munthe-Kaas and Crouch–Grossman methods in the solution of some mechanical problems. These methods are quite new, and they exploit intrinsic properties of the manifolds defined by the mechanical problems, thus ensuring that the numerical solution obey underlying constraints. A brief introduction to the methods is presented, and numerical simulations show some of the properties they possess. We also discuss error estimation and stepsize selection for some of these methods.

Composite materials with titanium-alloy matrix are currently the class of material with the highest specific resistance at temperatures up to 800 °C. The main hurdle to their application is their final cost. Even if it is clear that the... more

Composite materials with titanium-alloy matrix are currently the class of material with the highest specific resistance at temperatures up to 800 °C. The main hurdle to their application is their final cost. Even if it is clear that the costs of constituent materials are decreasing due to volume production effects, the production processing costs remain high due to the batch production approach. Centro Sviluppo Materiali’s (CSM) efforts have focused on the manufacturing process in order to obtain an innovative solution to reduce the manufacturing costs with respect to the hot isostatic pressing (HIP) process that represents the standard production process for this class of materials. The new approach can allow a cost reduction of about 40%; this result was obtained by developing an experimental “diffusion bonding” plant for co-rolling at high temperature in a superplastic rolling regime, sheets of titanium alloy and monofilament silicon carbide fabrics. The experimental pilot plant was proposed for patent with RM2006A000261 in May 2006. This paper describes the manufacturing phases and process results. Moreover, has been shown that the diffusion in the solid state was obtained in a process window that was at least 100 times faster than that of HIP. High-temperature tensile tests were carried out on specimens machined from metallic matrix composite materials produced with the roll-diffusion bonding (RDB) process. The samples produced were also submitted to electrochemical dissolution tests of the metallic matrix in order to verify the geometric integrity of the fibers inside the matrix after the bonding phase. The results achieved as well as the process knowledge acquired with the CSM pilot plant are the base for further development of industrial application of the titanium roll-diffusion bonding.

The energy preserving average vector field (AVF) method is applied to the coupled Schrödinger–KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order... more

The energy preserving average vector field (AVF) method is applied to the coupled Schrödinger–KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.