Controlled precision volume integration

1992 ◽  
Author(s):  
Kevin Novins ◽  
James Arvo
Keyword(s):  
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.

VolumeEVM: A new approach for surface/volume integration

2005 ◽  
Vol 29 (2) ◽  
pp. 217-224 ◽  
Author(s):  
J. Rodríguez ◽  
D. Ayala ◽  
S. Grau
Keyword(s):  
New Approach ◽  
Volume Integration

scholarly journals FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS

2019 ◽  
Vol 12 (2) ◽  
pp. 651-676 ◽  
Author(s):  
Christian Kühnlein ◽  
Willem Deconinck ◽  
Rupert Klein ◽  
Sylvie Malardel ◽  
Zbigniew P. Piotrowski ◽  
...  
Keyword(s):  
Finite Volume ◽  
Numerical Weather Prediction ◽  
Weather Prediction ◽  
Implicit Time ◽  
Integration Scheme ◽  
Advective Transport ◽  
Numerical Weather ◽  
Time Stepping ◽  
Spectral Transform ◽  
Volume Integration

Abstract. We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

Cell-based volume integration for boundary integral analysis

2012 ◽  
Vol 90 (7) ◽  
pp. 915-927 ◽  
Author(s):  
Matthew Koehler ◽  
Ruoke Yang ◽  
L.J. Gray
Keyword(s):  
Boundary Integral ◽  
Integral Analysis ◽  
Volume Integration

Design and Control of a Compact Light-Weight Planar Positioner Moving Over a Concentrated-Field Magnet Matrix

2011 ◽  
Author(s):  
Vu Huy Nguyen ◽  
Won-jong Kim
Keyword(s):  
Center Of Mass ◽  
Vertical Axis ◽  
Compact Size ◽  
Pi Controllers ◽  
Volume Integration ◽  
Two Phases ◽  
And Control ◽  
Reduced Power Consumption ◽  
Force Calculation ◽  
Lorentz Force Law

In this paper, a single-moving-part planar positioner with 6 coils is designed and implemented. A concentrated-field permanent-magnet matrix is employed as the stationary part. The moving platen has a compact size (185.4 mm × 157.9 mm), light mass (0.64 kg) and low center of mass. The moving platen carries three planar-motor armatures with two phases per motor. Force calculation is based on the Lorentz force law and conducted by volume integration. In order to deal with the nonlinearity due to trigonometric terms in the force-current relation, modified PID (proportional-integral-derivative) and lead-and-PI controllers are designed with computed currents to close the control loop and obtain the desired performances. Experimental results verify the commutation law and the force calculation. The new design with only 6 coils allows for simplification of the control algorithm and reduced power consumption of the positioner. The maximum travel ranges in x, y, and the rotation about the vertical axis are 15.24 cm, 20.32 cm, and 12.03°, respectively. The positioning resolution in x and y is 8 μm with the root-mean-square (rms) position noise of 6 μm. The positioning resolution in rotations about the vertical axis is 100 μrad.

Asymptotically Consistent Numerical Approximation of Hemolysis

2006 ◽  
Vol 128 (5) ◽  
pp. 688-696 ◽  
Author(s):  
Marie-Isabelle Farinas ◽  
André Garon ◽  
David Lacasse ◽  
Donatien N’dri
Keyword(s):  
Shear Stress ◽  
Medical Devices ◽  
Numerical Approximation ◽  
Damage Function ◽  
Computational Domain ◽  
In Vitro Experiments ◽  
Blood Damage ◽  
Volume Integration ◽  
Consistent Approach

In a previous communication, we have proposed a numerical framework for the prediction of in vitro hemolysis indices in the preselection and optimization of medical devices. This numerical methodology is based on a novel interpretation of Giersiepen-Wurzinger blood damage correlation as a volume integration of a damage function over the computational domain. We now propose an improvement of this approach based on a hyperbolic equation of blood damage that is asymptotically consistent. Consequently, while the proposed correction has yet to be proven experimentally, it has the potential to numerically predict more realistic red blood cell destruction in the case of in vitro experiments. We also investigate the appropriate computation of the shear stress scalar of the damage fraction model. Finally, we assess the validity of this consistent approach with an analytical example and with some 3D examples.

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