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Computational Electromagnetics with the RBF-FD Method

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arXiv 2023年

作者： Kolar-Požun, Andrej Kosec, Gregor Parallel and Distributed Systems Laboratory ’Jožef Stefan’ Institute Ljubljana Slovenia Faculty of Mathematics and Physics University of Ljubljana Ljubljana Slovenia

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Di... 详细信息

关键词： Computational electromagnetics

Characterizing the Dilemma of Performance and Index Size in Billion-Scale Vector Search and Breaking It with Second-Tier Memory

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arXiv 2024年

作者： Cheng, Rongxin Peng, Yifan Wei, Xingda Xie, Hongrui Chen, Rong Shen, Sijie Chen, Haibo Institute of Parallel and Distributed Systems SEIEE Shanghai Jiao Tong University China Shanghai AI Laboratory China Alibaba Group China

Vector searches on large-scale datasets are critical to modern online services like web search and RAG, which necessity storing the datasets and their index on the secondary storage like SSD. In this paper, we are the first to characterize the trade-off of performance and index size in existing SSD-based graph and cluster indexes: to improve throughput by 5.7 × and 1.7 ×, these indexes have to pay a 5.8 × storage amplification and 7.7 × with respect to the dataset size, respectively. The root cause is that the coarse-grained access of SSD mismatches the fine-grained random read required by vector indexes with small amplification. This paper argues that second-tier memory, such as remote DRAM/NVM connected via RDMA or CXL, is a powerful storage for addressing the problem from a system’s perspective, thanks to its fine-grained access granularity. However, putting existing indexes—primarily designed for SSD—directly on second-tier memory cannot fully utilize its power. Meanwhile, second-tier memory still behaves more like storage, so using it as DRAM is also inefficient. To this end, we build a graph and cluster index that centers around the performance features of second-tier memory. With careful execution engine and index layout designs, we show that vector indexes can achieve optimal performance with orders of magnitude smaller index amplification, on a variety of second-tier memory devices. Based on our improved graph and vector indexes on second-tier memory, we further conduct a systematic study between them to facilitate developers choosing the right index for their workloads. Interestingly, the findings on the second-tier memory contradict the ones on SSDs. © 2024, CC BY.

关键词： Dynamic random access storage

Transactional Indexes on (RDMA or CXL-based) Disaggregated Memory with Repairable Transaction

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arXiv 2023年

作者： Wei, Xingda Wang, Haotian Wang, Tianxia Chen, Rong Gu, Jinyu Zuo, Pengfei Chen, Haibo Institute of Parallel and Distributed Systems SEIEE Shanghai Jiao Tong University China Shanghai AI Laboratory China Huawei Cloud China

The failure atomic and isolated execution of clients operations is a default requirement for a system that serve multiple loosely coupled clients at a server. However, disaggregated memory breaks this requirement in remote indexes because a client operation is disaggregated to multiple remote reads/writes. Current indexes focus on performance improvements and largely ignore tolerating client failures. We argue that a practical DM index should be transactional: each index operation should be failure atomic and isolated in addition to being concurrency isolated. We present repairable transaction (rTX), a lightweight primitive to execute DM index operations. Each rTX can detect other failed rTXes on-the-fly with the help of concurrency control. Upon detection, it will repair their non-atomic updates online with the help of logging, thus hiding their failures from healthy clients. By further removing unnecessary logging and delegating concurrency control to existing carefully-tuned index algorithms, we show that transactional indexes can be built at a low performance overhead on disaggregated memory. We have refactored two state-of-the-art DM indexes, RaceHashing and Sherman (B+Tree), with rTX. Evaluations show that rTX is 1.2–2× faster than other alternatives, e.g., distributed transaction. Meanwhile, its overhead is up to 42% compared to non-fault-tolerant indexes. © 2023, CC BY.

关键词： Concurrency control

A general and scalable solution for heterogeneous workflow invocation and nesting

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A general and scalable solution for heterogeneous workflow i...

Workshop on Workflows in Support of Large-Scale Science, WORKS

作者： Tamas Kukla Tamas Kiss Gabor Terstyanszky Peter Kacsuk Centre for Parallel Computing School of Informatics University of Westminster London UK Laboratory of the Parallel and Distributed Systems Computer and Automation Research Institute Hungarian Academy of Sciences (ATOMKI) Budapest Hungary

Several widely utilized, grid workflow management systems emerged in the last decade. These systems were developed by different scientific communities for various purposes. Enhancing these systems with the capability of invoking and nesting the workflows of other systems within their native workflows makes these communities to be able to carry out cross-organizational experiments and share non-native workflows. The novel solution described in this paper allows the integration of different workflow engines and makes them accessible for workflow systems in order to achieve this goal. The solution is based on an application repository and submitter, which exposes different workflow engines and executes them using the computational resources of the grid. In contrast with other approaches, our solution is scalable in terms of both number of workflows and amount of data, easily extendable in the sense that the integration of a new workflow engine does not require code re-engineering, and general, since it can be adopted by numerous workflow systems.

关键词： Engines Workflow management software Risk management Petri nets parallel processing Informatics Laboratories Concurrent computing distributed computing Automation

A superconvergence result in the RBF-FD method

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arXiv 2024年

作者： Kolar-Požun, Andrej Jančič, Mitja Kosec, Gregor Parallel and Distributed Systems Laboratory Jožef Stefan Institute Ljubljana Slovenia Faculty of Mathematics and Physics University of Ljubljana Ljubljana Slovenia

Radial Basis Function-generated Finite Differences (RBF-FD) is a meshless method that can be used to numerically solve partial differential equations. The solution procedure consists of two steps. First, the differential operator is discretised on given scattered nodes and afterwards, a global sparse matrix is assembled and inverted to obtain an approximate solution. Focusing on Polyharmonic Splines as our Radial Basis Functions (RBFs) of choice, appropriately augmented with monomials, it is well known that the truncation error of the differential operator approximation is determined by the degree of monomial augmentation. Naively, one might think that the solution error will have the same order of convergence. We present a superconvergence result that shows otherwise - for some augmentation degrees, order of convergence is higher than expected. © 2024, CC BY.

关键词： Finite difference method

Computational Electromagnetics with the RBF-FD Method

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Computational Electromagnetics with the RBF-FD Method

International Multidisciplinary Conference on Computer and Energy Science (SpliTech)

作者： Andrej Kolar-Požun Gregor Kosec Parallel and Distributed Systems Laboratory ’Jožef Stefan’ Institute Ljubljana Slovenia Faculty of Mathematics and Physics University of Ljubljana Ljubljana Slovenia

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We introduce its generalisation to a meshless setting using the Radial Basis Function gene...

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parallel point sampling for 3D bodies

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Parallel point sampling for 3D bodies

Proceedings of the International Convention MIPRO

作者： Urban Duh Matjaž Depolli Jure Slak Gregor Kosec Parallel and Distributed Systems Laboratory “Jožef Stefan” Institute Ljubljana Slovenia Faculty of Mathematics and Physics University of Ljubljana Ljubljana Slovenia

ISBN: (数字)9789532330991

ISBN: (纸本)9781728153391

Point sampling in interiors and on surfaces of 3D bodies has important applications in computer graphics, visualization and physical simulations. Some of those application require certain statistical properties of the generated sample, but many don't and it is often only desired that the final points are distributed quasi regularly, with approximately equal distances to the neighboring points. We present a parallel version of an algorithm for point sampling that supports generation of locally regular point sets, but with globally variable point spacing. The behavior of the algorithm is show-cased on interiors and surfaces of 2D and 3D models. The speedups of the parallel execution are also reported.

关键词： Solid modeling Visualization Three-dimensional displays Design automation Two dimensional displays Approximation algorithms parallel algorithms

Natural Convection of Non-Newtonian Fluids in a Differentially Heated Closed Cavity

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Natural Convection of Non-Newtonian Fluids in a Differential...

Proceedings of the International Convention MIPRO

作者： Miha Rot Gregor Kosec “Jožef Stefan” Institute Parallel and Distributed Systems Laboratory Ljubljana Slovenia Jožef Stefan” International Postgraduate School Ljubljana Slovenia

Fluids in computational hydrodynamics are often considered Newtonian, meaning a constant viscosity, but that is just a crude approximation for many real-world examples. Accounting for Non-Newtonian behaviour can provide a significant improvement in simulation accuracy. We present a meshless solution for the natural convection of a power-law non-Newtonian fluid driven by differentially heated cavity walls. The Navier-Stokes and heat transport equations are coupled using the Boussinesq approximation and numerically solved with the generalized finite differences, explicit Euler stepping and Chorin's projection method.

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Stability analysis of RBF-FD and WLS based local strong form meshless methods on scattered nodes

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arXiv 2022年

作者： Jančić, Mitja Kosec, Gregor 'Jožef Stefan' Institute Parallel and Distributed Systems Laboratory Ljubljana Slovenia 'Jožef Stefan' International Postgraduate School Ljubljana Slovenia

The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the approximation order and basis functions. In this paper we analyse two popular variants of local strong form meshless methods, namely the radial basis function-generated finite differences (RBF-FD) using polyharmonic splines (PHS) augmented with monomials, and the weighted least squares (WLS) approach using only monomials. Our analysis focuses on the accuracy and stability of the numerical solution computed on scattered nodes in a two- and three-dimensional domain. We show that while the WLS variant is a better choice when lower order approximations are sufficient, the RBF-FD variant exhibits a more stable behavior and a higher accuracy of the numerical solution for higher order approximations, but at the cost of higher computational complexity. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite difference method