Engineers at the University of California, San Diego, have developed a new family of methods to significantly increase the speed of time-resolved numerical simulations in computational grand challenge problems.
Such problems often arise from the high-resolution approximation of the partial differential equations governing complex flows of fluids or plasmas. The breakthrough could be applied to simulations that include millions or billions of variables, including turbulence simulations.
Modern computers are generally built from commodity hardware developed for serving and surfing the web. When applied to cutting-edge problems in scientific computing, computers built from such general-purpose hardware usually spend most of their time moving data around in memory, and the hardware dedicated to floating point computations (that is, the actual addition and multiplication of numbers) spends most of its time idle.
The small memory footprint of the new schemes developed at UC San Diego means that numerical problems of a given size will run much faster on a given computer, and that even larger numerical problems may be considered.
"Moving information around in memory is the bottleneck in almost all large-scale numerical simulations today," said Thomas Bewley, a mechanical engineering professor who leads the Flow Control Lab at the Jacobs School of Engineering at UC San Diego.
"The remarkable feature of the new family of schemes developed in this work is that they require significantly less memory in the computer for a given size simulation problem than existing high-order methods of the same class, while providing excellent numerical stability, accuracy, and computational efficiency."
Complex systems such as flows of fluids and plasmas generally evolve as a result of a combination of physical effects, such as diffusion and convection. Some of these effects are linear and incorporate many spatial derivatives (that is, they are characterized by a large range of characteristic time scales, and are thus referred to as "stiff"). These terms are best handled with "implicit" methods, which require the solution of many simple simultaneous equations using matrix algebra and iterative solvers.
Other effects are nonlinear and incorporate fewer spatial derivatives (that is, they are characterized by a smaller range of characteristic time scales, and are thus referred to as "nonstiff"). These terms are most easily handled with explicit methods, which treat the propagation of each equation independently. If the stiff terms are treated with explicit methods, a severe restriction arises on the timestep, which slows the simulation; if the nonstiff terms are treated with implicit methods, complex and computationally expensive iterative solvers must be used.
The new "implicit/explicit" or IMEX time marching schemes developed at UC San Diego thus marry together two algorithms for time-resolved simulations of the standard "Runge-Kutta" or RK form. The implicit algorithm is applied to the stiff terms of the problem, and the explicit algorithm is applied to the nonstiff terms of the problem. The two algorithms so joined are each endowed with good numerical properties, such as excellent stability and high accuracy, and, notably, maintain this high accuracy when working together in concert. The compatible pairs of simulation methods so developed are known as IMEXRK schemes.
"Searching for the right combination of the dozens of parameters that make these new IMEXRK algorithms work well was like finding a needle in a haystack, and required a tedious search over a very large parameter space, combined with the delicate codification of various numerical intuition to simplify the search. It took almost one year to complete," said Daniele Cavaglieri, a Ph.D. student and co-author of the paper.
Researchers describe the new methods in the January 2015 issue of the Journal of Computational Physics.
Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional OED systems: http://www.
Ioana Patringenaru | EurekAlert!
Underwater acoustic localization of marine mammals and vehicles
23.11.2017 | IMDEA Networks Institute
NASA CubeSat to test miniaturized weather satellite technology
10.11.2017 | NASA/Goddard Space Flight Center
High-precision measurement of the g-factor eleven times more precise than before / Results indicate a strong similarity between protons and antiprotons
The magnetic moment of an individual proton is inconceivably small, but can still be quantified. The basis for undertaking this measurement was laid over ten...
Heat from the friction of rocks caused by tidal forces could be the “engine” for the hydrothermal activity on Saturn's moon Enceladus. This presupposes that...
The WHO reports an estimated 429,000 malaria deaths each year. The disease mostly affects tropical and subtropical regions and in particular the African continent. The Fraunhofer Institute for Silicate Research ISC teamed up with the Fraunhofer Institute for Molecular Biology and Applied Ecology IME and the Institute of Tropical Medicine at the University of Tübingen for a new test method to detect malaria parasites in blood. The idea of the research project “NanoFRET” is to develop a highly sensitive and reliable rapid diagnostic test so that patient treatment can begin as early as possible.
Malaria is caused by parasites transmitted by mosquito bite. The most dangerous form of malaria is malaria tropica. Left untreated, it is fatal in most cases....
The formation of stars in distant galaxies is still largely unexplored. For the first time, astron-omers at the University of Geneva have now been able to closely observe a star system six billion light-years away. In doing so, they are confirming earlier simulations made by the University of Zurich. One special effect is made possible by the multiple reflections of images that run through the cosmos like a snake.
Today, astronomers have a pretty accurate idea of how stars were formed in the recent cosmic past. But do these laws also apply to older galaxies? For around a...
Just because someone is smart and well-motivated doesn't mean he or she can learn the visual skills needed to excel at tasks like matching fingerprints, interpreting medical X-rays, keeping track of aircraft on radar displays or forensic face matching.
That is the implication of a new study which shows for the first time that there is a broad range of differences in people's visual ability and that these...
15.11.2017 | Event News
15.11.2017 | Event News
30.10.2017 | Event News
24.11.2017 | Physics and Astronomy
24.11.2017 | Health and Medicine
24.11.2017 | Earth Sciences