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TIME-PARALLEL COMPUTATION OF PSEUDO-ADJOINTS FOR A LEAPFROG SCHEME

CHRISTIAN H. BISCHOF, H. MARTIN BÜCKER, PO-TING WU
2004 International journal of high speed computing  
The leapfrog scheme is a commonly used second-order di erence scheme for solving di erential equations.  ...  If Z (t) denotes the state of the system at time t, the leapfrog scheme computes the state at the next time step as Z (t + 1) = H (Z(t); Z (t ?  ...  Acknowledgments We thank David Zhi Wang of the Center for Analysis and Prediction of Storms at the University of Oklahoma for providing us with the code for the shallow water equation model.  ... 
doi:10.1142/s0129053304000219 fatcat:btxlis4m7fdjfpzawtg5vsc67e

Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations [article]

Fernando Casas, Philippe Chartier, Alejandro Escorihuela-Tomas, Yong Zhang
2020 arXiv   pre-print
In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis.  ...  It is shown in particular that the new integrators are symmetric and symplectic up to high orders if one uses a symmetric and symplectic basic method.  ...  PC acknowledges funding by INRIA through its Sabbatical program and thanks the University of the Basque Country for its hospitality.  ... 
arXiv:2005.12893v1 fatcat:refw4zuvjbf5hgx4rlb4u457gm

Time-domain seismic modeling in viscoelastic media for full waveform inversion on heterogeneous computing platforms with OpenCL

Gabriel Fabien-Ouellet, Erwan Gloaguen, Bernard Giroux
2017 Computers & Geosciences  
We present a program called SeisCL for 2D and 3D viscoelastic FWI in the time 12 domain.  ...  Modeling the wave propagation for realistic scenarios is computationally intensive, 8 which limits the applicability of FWI.  ...  half-time steps in a classic leapfrog fashion.  ... 
doi:10.1016/j.cageo.2016.12.004 fatcat:2j57qpasmvac5eiodlsa6tdp3u

Automatic Differentiation, Tangent Linear Models, and (Pseudo)Adjoints1 [chapter]

Christian H. Bischof
1995 High Performance Computing in the Geosciences  
We also present a novel approach to the computation of gradients that uses a reverse mode approach at the time loop level and a forward mode a p p r o d at every time step.  ...  Derivatives provide a way for computing a relatively simple approximation of F, thus allowing one to inexpensively explore the behavior o f f in the neighborhood of po.  ...  of the sensitivity-enhanced version of the MM5 code.  ... 
doi:10.1007/978-94-011-0033-5_5 fatcat:4cvhxfqzxrgkhoddtljr4uu6ve

Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations

Fernando Casas, Philippe Chartier, Alejandro Escorihuela-Tomàs, Yong Zhang
2020 Journal of Computational and Applied Mathematics  
In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis.  ...  It is shown in particular that the new integrators are symmetric and symplectic up to high orders if one uses a symmetric and symplectic basic method.  ...  PC acknowledges funding by INRIA, France through its Sabbatical program and thanks the University of the Basque Country for its hospitality.  ... 
doi:10.1016/j.cam.2020.113006 fatcat:iac3qf67abckrphya2alfkx3g4

Functional probabilistic programming for scalable Bayesian modelling [article]

Jonathan Law, Darren Wilkinson
2019 arXiv   pre-print
Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents.  ...  Bayesian models are useful when an experiment has only a small number of observations and in applications where transparency of data driven decisions is important.  ...  Acknowledgements JL is supported by the Engineering and Physical Sciences Research Council, Centre for Doctoral Training in Cloud Computing for Big Data (grant number EP/L015358/1) and Digital Catapult  ... 
arXiv:1908.02062v1 fatcat:2kzvdgrferadxaj7bksnjibqua

Hamiltonian Monte Carlo with Asymmetrical Momentum Distributions [article]

Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki
2021 arXiv   pre-print
In our framework, we show that plain HMC with asymmetrical momentum distributions breaks a key self-adjointness requirement.  ...  We present a novel convergence analysis for HMC utilizing new analytic and probabilistic arguments.  ...  Ricci curvature of a Riemannian manifold is interpreted as a measure of deformation along parallel transformations. Definition 2.  ... 
arXiv:2110.12907v1 fatcat:zcxtgeoowjh7xouzn5v4hbifvm

Hamiltonian Monte Carlo solution of tomographic inverse problems

Andreas Fichtner, Andrea Zunino, Lars Gebraad
2018 Geophysical Journal International  
This allows us to solve a fully nonlinear, probabilistic traveltime tomography with several thousand unknowns on a standard laptop computer, without any need for supercomputing resources.  ...  Most importantly, we demonstrate the combination of HMC with adjoint techniques.  ...  Despite this computational overhead, our HMC runs for several thousand free parameters did not require any parallel computing.  ... 
doi:10.1093/gji/ggy496 fatcat:d47z7s6x25eejgnk63zdzbkwkq

Parallel multigrid summation for the -body problem

Jesús A. Izaguirre, Scott S. Hampton, Thierry Matthey
2005 Journal of Parallel and Distributed Computing  
MG is based on a hierarchical decomposition of computational kernels on multiple grids.  ...  The method can be combined with multiple time stepping integrators to produce a powerful simulation protocol for simulation of biological molecules and other materials.  ...  Skeel for sharing details of their vacuum multigrid summation implementation, which allowed cross-verification of our implementation. Chengbang Huang generated many of the plots in this  ... 
doi:10.1016/j.jpdc.2005.03.006 fatcat:tg6oz2airbf7rjp4fpmbogul3e

On the maximum time step in weakly compressible SPH

Damien Violeau, Agnès Leroy
2014 Journal of Computational Physics  
The influence of time integration scheme is also studied, and proved to be prominent. All of the above theoretical developments give excellent agreement against numerical results.  ...  We then extend the theory in order to study the influence of the method used to compute the density, of the gradient and divergence SPH operators, of background pressure, of the model used for viscous  ...  Theory, sequential first-order scheme Theory, leapfrog scheme p + =0.0 Theory, leapfrog scheme p + =0.14 Theory, leapfrog scheme p + =2.0 Numerical, leapfrog scheme, infinite flow p + =0.0 Numerical, leapfrog  ... 
doi:10.1016/j.jcp.2013.09.001 fatcat:clugyiec5bg3jeq6duzj43lglq

Explicit methods in extended phase space for inseparable Hamiltonian problems

Pauli Pihajoki
2014 Celestial mechanics & dynamical astronomy  
We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space.  ...  Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator.  ...  Acknowledgements I am grateful to the anonymous reviewers for suggestions and comments that have greatly improved this article.  ... 
doi:10.1007/s10569-014-9597-9 fatcat:hikrnbvu7bdllhsqcf5xel3gzu

An MCMC Method for Uncertainty Set Generation via Operator-Theoretic Metrics [article]

Anand Srinivasan, Naoya Takeishi
2020 arXiv   pre-print
We adapt Hamiltonian Monte Carlo for sampling high-dimensional transfer operators in a computationally efficient manner.  ...  In this paper, we propose a method for model uncertainty set generation via Markov chain Monte Carlo.  ...  Heuristic: parallel HMC with uniform prior The mixing time of HMC is highly sensitive to the choice of discretization parameters (in particular, n leapfrog, step size).  ... 
arXiv:2006.03795v2 fatcat:jyk3lwfsajftzngsusehtrhfje

Parallel software for lattice N = 4 supersymmetric Yang–Mills theory

David Schaich, Thomas DeGrand
2015 Computer Physics Communications  
We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development.  ...  We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional N = 4 supersymmetric Yang--Mills theory with gauge group SU(N).  ...  This approach is much more computationally efficient, allowing for two dimensions to be dropped completely, at the cost of some code duplication.  ... 
doi:10.1016/j.cpc.2014.12.025 fatcat:a46j7mr7effghfcg2pp7qtupy4

Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations [article]

Timo Schorlepp, Tobias Grafke, Sandra May, Rainer Grauer
2022 arXiv   pre-print
Most likely configurations are computed by numerically finding the highest probability velocity field realising an extreme constraint as solution of a large optimisation problem.  ...  In particular, we are able to demonstrate that artificially enforcing rotational symmetry for large strain configurations leads to a severe underestimate of their probability, as it is dominated in likelihood  ...  Von Neumann stability analysis of the Leapfrog scheme for the linear advection equation shows the existence of the so-called computational mode, leading to even-odd-oscillations in the time domain at a  ... 
arXiv:2107.06153v2 fatcat:en7j75luu5grbhgc6tutz5rd3y

A new adiabatic kernel for the MC2 model

S.J. Thomas, C. Girard, R. Benoit, M. Desgagné, P. Pellerin
1998 ATMOSPHERE-OCEAN  
The computational efþciency of the model is reported for 1D Jacobi and 3D Alternating Direction Implicit (ADI) line relaxation preconditioners implemented with a parallel data transposition strategy. |  ...  advection scheme.  ...  An A-grid version of the line Jacobi scheme was þrst implemented in the EULAG  ... 
doi:10.1080/07055900.1998.9649613 fatcat:hylsdlqepnco3j5clnoudhy43e
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