Generating the Voronoi-Delaunay Dual Diagram for Co-Volume Integration Schemes

2007 ◽  
Author(s):  
Igor Sazonov ◽  
Oubay Hassan ◽  
Ken Morgan ◽  
Nigel P. Weatherill
Keyword(s):  
Integration Schemes ◽  
Volume Integration

Smooth Delaunay-Voronoï Dual Meshes for Co-Volume Integration Schemes

2007 ◽  
pp. 529-541 ◽  
Author(s):  
Igor Sazonov ◽  
Oubay Hassan ◽  
Kenneth Morgan ◽  
Nigel P. Weatherill
Keyword(s):  
Integration Schemes ◽  
Volume Integration

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Air Bridge Technology: A Comparison of Novel Interconnect Materials and Integration Schemes for Beyond 45 nm

2003 ◽  
Vol 766 ◽  
Author(s):  
Kenneth Foster ◽  
Joost Waeterloos ◽  
Don Frye ◽  
Steve Froelicher ◽  
Mike Mills
Keyword(s):  
Dielectric Constants ◽  
Advanced Technology ◽  
Effective Dielectric Constant ◽  
Device Performance ◽  
Interlayer Dielectric ◽  
Integration Schemes ◽  
Stepwise Reduction ◽  
Bridge Technology ◽  
Integrated Device ◽  
Compare And Contrast

AbstractThe electronics industry, in a continual drive for improved integrated device performance, is seeking increasingly lower dielectric constants (k) of the insulators that are used as interlayer dielectric (ILD) for advanced logic interconnects. As the industry continually seeks a stepwise reduction of the “effective” dielectric constant (keff), simple extendibility, leads to the consideration of the highest performance possible, namely air bridge technology. In this paper we will discuss requirements, integration schemes and properties for a novel class of materials that has been developed as part of an advanced technology probe into air bridge architecture. We will compare and contrast these potential technology offerings with other existing dense and porous ILD integration options, and show that the choice is neither trivial nor obvious.

Challenges and Benefits of Product-Like SRAM in Technology Development

2011 ◽  
Author(s):  
Felix Beaudoin ◽  
Stephen Lucarini ◽  
Fred Towler ◽  
Stephen Wu ◽  
Zhigang Song ◽  
...  
Keyword(s):  
Technology Development ◽  
Random Access ◽  
Random Access Memory ◽  
Static Random Access Memory ◽  
Development Phase ◽  
High Complexity ◽  
Access Memory ◽  
Integration Schemes ◽  
Front End

Abstract For SRAMs with high logic complexity, hard defects, design debug, and soft defects have to be tackled all at once early on in the technology development while innovative integration schemes in front-end of the line are being validated. This paper presents a case study of a high-complexity static random access memory (SRAM) used during a 32nm technology development phase. The case study addresses several novel and unrelated fail mechanisms on a product-like SRAM. Corrective actions were put in place for several process levels in the back-end of the line, the middle of the line, and the front-end of the line. These process changes were successfully verified by demonstrating a significant reduction of the Vmax and Vmin nest array block fallout, thus allowing the broader development team to continue improving random defectivity.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Projected explicit and implicit Taylor series methods for DAEs

2021 ◽  
Author(s):  
Diana Estévez Schwarz ◽  
René Lamour
Keyword(s):  
Taylor Series ◽  
Multibody Systems ◽  
Optimization Problem ◽  
Automatic Differentiation ◽  
Taylor Coefficients ◽  
Integration Schemes ◽  
Consistent Initial Values ◽  
Taylor Series Methods ◽  
Systems Simulation ◽  
Derivative Array

AbstractThe recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization opens new possibilities to apply Taylor series integration methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted to DAEs of arbitrary index. Owing to our formulation as a projected optimization problem constrained by the derivative array, no explicit description of the inherent dynamics is necessary, and various Taylor integration schemes can be defined in a general framework. In particular, we address higher-order Padé methods that stand out due to their stability. We further discuss several aspects of our prototype implemented in Python using Automatic Differentiation. The methods have been successfully tested on examples arising from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.

ODE integration schemes for plane-wave real-time time-dependent density functional theory

2019 ◽  
Vol 150 (1) ◽  
pp. 014101 ◽  
Author(s):  
Daniel A. Rehn ◽  
Yuan Shen ◽  
Marika E. Buchholz ◽  
Madan Dubey ◽  
Raju Namburu ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Plane Wave ◽  
Real Time ◽  
Density Functional ◽  
Time Dependent ◽  
Functional Theory ◽  
Integration Schemes ◽  
Dependent Density
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