Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1901.00229

The Divide-and-Conquer Framework: A Suitable Setting for the DDM of the Future

Ismael Herrera-Revilla·Iván Contreras·Graciela S. Herrera
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper was prompted by numerical experiments we performed, in which algorithms already available in the literature (DVS-BDDM) yielded accelerations (or speedups) many times larger (more than seventy in some examples already treated, but probably often much larger) than the number of processors used. Based on these outstanding results, here it is shown that believing in the standard ideal speedup, which is taken to be equal to the number of processors, has limited much the performance goal sought by research on domain decomposition methods (DDM) and has hindered much its development, thus far. Hence, an improved theory in which the speedup goal is based on the Divide and Conquer algorithmic paradigm, frequently considered as the leitmotiv of domain decomposition methods, is proposed as a suitable setting for the DDM of the future.

Explore related subjects

cs.CEcs.NAmath.NAphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ismael Herrera-Revilla, Iván Contreras, Graciela S. Herrera. 2019-01-02. The Divide-and-Conquer Framework: A Suitable Setting for the DDM of the Future. https://arxiv.org/abs/1901.00229

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Element-dependent buckling loads of stiffened panels under cantilevered shear

The linearized buckling load of a stiffened panel depends on the stress stiffness its shell element assembles. We read it from exported operators against three truncations of one second variation. The classic pass of ANSYS SHELL181 carries a rotation-rotation block pairing the drilling freedom with the bending rotations and its perturbation pass does not; removing the block recovers the perturbation load factor to 0.02%. SHELL281 carries block and couplings in both passes. Abaqus S4 matches the critical mode of the complete second variation to 1.0000 on the translations and its load factor to 1.7%, against 17% and 34% for the other two forms. On an optimized panel under cantilevered shear a 20-node continuum lies 3% to 6% above that form, S4 and SHELL281, 11% and 23% below both SHELL181 passes and 25% above Abaqus S8R, at the finest meshes. On a conventionally stiffened panel the SHELL181 passes stand 1.0% and 3.5% above the complete form, 9% and 21% at half the rib pitch; under a shear flow, on cylinders, open beams and under axial compression the three forms coincide and no pass parts by more than 0.3%.

cs.CE↗
arXiv2026

Pragmatic Information, Computation, and the Efficient Market Hypothesis

The efficient market hypothesis, that prices reflect all available information, imputes a meaning to market moving information, a view of information foreign to standard information theory. Here, after reviewing properties that make a proposed formula for ``pragmatic information" a plausible measure of meaning, we consider the role that the receiver's position in the machine hierarchy corresponding to the Chomsky hierarchy play in extracting this meaning. We show that a receiver at a given level in the hierarchy may be unable to extract pragmatic information from a message because it appears random, yet a receiver at a higher level in the hierarchy finds the message perfectly intelligible. Also, the maximum processing rates for messages of different levels of hierarchy serve as a kind of channel capacity, leading to a tradeoff between the amount of pragmatic information extracted and the extraction time. All of the above suggests a recasting of market efficiency in terms of ``computational efficiency'', i.e. the question of whether a market appears efficient to a participant with a given computational endowment. Successful trading strategies implementable as finite state machines, the lowest level in the hierarchy, imply departures from ``finite state efficiency''. We show, via a stylized example, how pragmatic information can characterize the ensuing approach to finite state efficiency. We also show that actual market dynamics can be more computationally intractable than any finite state machine can process by proving the PSPACE-completeness of the processing of the smart order routing systems of major brokerage firms. We conclude that computational efficiency is the norm and pragmatic information can characterize any departure from it.

cs.CE↗
arXiv2026

Synthetic Human Mobility Data Generation: A Structured Review of Representations, Methods, and Practical Capabilities

Human mobility data has become an increasingly important component of urban analytics. Although the range of available mobility data sources has expanded substantially, access remains highly constrained by commercial restrictions, privacy concerns, and institutional barriers. Data protection procedures also often reduce the analytical value of released datasets. Synthetic mobility data has emerged as a promising solution, but existing methods differ substantially in their underlying mechanisms, the information they preserve, the outputs they generate, and the analytical questions they can support. Their comparative strengths and trade-offs remain insufficiently understood for urban analytics. This paper presents a structured review of synthetic human mobility data generation from an urban analytics perspective. We review the literature by methodological family and index it by the mobility outputs each family generates natively and the analytical capabilities those outputs enable. We first provide a taxonomy of synthetic data products, including population and persona representations, activity schedules, trip and tour records, trajectories, and aggregate mobility patterns. We then review the major methodological families, spanning mechanistic models, survey-driven population synthesis, activity- and agent-based simulation, deep generative models, transformer-based mobility language models, and LLM-agentic systems. Building on this synthesis, we introduce a Meaning-Population-Autonomy framework that characterises these methods along three dimensions: behavioural meaning, population grounding and scale, and generation autonomy. We consider these dimensions the principal requirements for downstream urban analytics. Few methods deliver behavioural meaning, population grounding and autonomous generation at once, and fewer still with generation constrained to feasible trajectories.

cs.CE↗