Hardware Adaptive High‐Order Interpolation for Real‐Time Graphics

2021 ◽  
Vol 40 (8) ◽  
pp. 1-16
Author(s):  
D. Lin ◽  
L. Seiler ◽  
C. Yuksel
Keyword(s):  
Real Time ◽  
High Order ◽  
High Order Interpolation

scholarly journals Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Qiang Chen ◽  
Jianyuan Xiao ◽  
Peifeng Fan
Keyword(s):  
Field Theory ◽  
Real Time ◽  
Quantum Electrodynamics ◽  
Symplectic Form ◽  
Strong Field ◽  
Relativistic Quantum ◽  
High Order ◽  
High Quality ◽  
Geometric Structures ◽  
Gauge Invariant

Abstract A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

scholarly journals A Predictive Technique for the Real-Time Trajectory Scaling under High-Order Constraints

2021 ◽  
pp. 1-1
Author(s):  
Corrado Guarinolobianco ◽  
Marco Faroni ◽  
Manuel Beschi ◽  
Antonio Visioli
Keyword(s):  
Real Time ◽  
High Order ◽  
The Real ◽  
Order Constraints

Real-time monitoring of hydrogel rheological property changes and gelation processes using high-order modes of cantilever sensors

2020 ◽  
Vol 128 (17) ◽  
pp. 174502
Author(s):  
Ellen Cesewski ◽  
Manjot Singh ◽  
Yang Liu ◽  
Junru Zhang ◽  
Alexander P. Haring ◽  
...  
Keyword(s):  
Rheological Property ◽  
Real Time ◽  
High Order ◽  
Real Time Monitoring ◽  
Cantilever Sensors ◽  
Property Changes

AUSM-Based High-Order Solution for Euler Equations

2012 ◽  
Vol 12 (4) ◽  
pp. 1096-1120 ◽  
Author(s):  
Angelo L. Scandaliato ◽  
Meng-Sing Liou
Keyword(s):  
Euler Equations ◽  
Splitting Method ◽  
High Order ◽  
Riemann Solvers ◽  
Carbuncle Phenomenon ◽  
Solution Accuracy ◽  
Matrix Vector ◽  
Approximate Riemann Solvers ◽  
Monotonicity Preserving ◽  
High Order Interpolation

AbstractIn this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme and its variations, and the monotonicity preserving (MP) scheme, for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM+-UP is also shown to be free of the so-called “carbuncle” phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables, even though they require additional matrix-vector operations. Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high order solutions is proposed; the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.

Exploring high-order adder compressors for power reduction in sum of absolute differences architectures for real-time UHD video encoding

2020 ◽  
Vol 17 (5) ◽  
pp. 1735-1754
Author(s):  
Guilherme Paim ◽  
Gustavo M. Santana ◽  
Brunno A. Abreu ◽  
Leandro M. G. Rocha ◽  
Mateus Grellert ◽  
...  
Keyword(s):  
Real Time ◽  
Power Reduction ◽  
High Order ◽  
Video Encoding

scholarly journals Comparison and real-time monitoring of high-order harmonic generation in different sources

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
J.-P. Brichta ◽  
M. C. H. Wong ◽  
J. B. Bertrand ◽  
H.-C. Bandulet ◽  
D. M. Rayner ◽  
...  
Keyword(s):  
Real Time ◽  
Harmonic Generation ◽  
High Order ◽  
Real Time Monitoring ◽  
High Order Harmonic Generation ◽  
High Order Harmonic ◽  
Different Sources

Assessment of Enhanced Multi-Dimensional Limiting Process for Multi-Dimensional Flows

2011 ◽  
Author(s):  
Kyu Hong Kim ◽  
Jung Ho Park
Keyword(s):  
Higher Order ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Interpolation Scheme ◽  
Local Extrema ◽  
Numerous Test ◽  
High Order Interpolation

In this paper, a new limiting process based on the Multi-dimensional Limiting Process, called enhanced Multi-dimensional Limiting Process is developed and tested with several cases. The enhanced Multi-dimensional Limiting Process, e-MLP has a number of useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. The new limiting process was applied to numerous test cases. Through these tests, we could confirm that e-MLP enhances the accuracy and efficiency with both continuous and discontinuous multidimensional flows.

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