Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEfficient and scalable data structures and algorithms for goal-oriented adaptivity of space-time FEM codes
58
0
0.0
(
0
)
Added by
Uwe K\\\"ocher
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space and time adaptive methods derived from the dual weighted residual (DWR) method appear to be a shiny key technology to generate optimal space-time meshes to minimise costs. Current implementations for challenging problems of numerical screening tools including the DWR technology broadly suffer in their extensibility to other problems, in high memory consumption or in missing system solver technologies. This work contributes to the efficient embedding of DWR space-time adaptive methods into numerical screening tools for challenging problems of physically relevance with a new approach of flexible data structures and algorithms on them, a modularised and complete implementation as well as illustrative examples to show the performance and efficiency.
rate research
Read More
The `equation-free toolbox empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because micro-scale simulations are often the best available description of a system. The methodology bypasses the derivation of macroscopic evolution equations by computing the micro-scale simulator only over short bursts in time on small patches in space, with bursts and patches well-separated in time and space respectively. We introduce the suite of coded equation-free functions in an accessible way, link to more detailed descriptions, discuss their mathematical support, and introduce a novel and efficient algorithm for Projective Integration. Some facets of toolbox development of equation-free functions are then detailed. Download the toolbox functions (https://github.com/uoa1184615/EquationFreeGit) and use to empower efficient and accurate simulation in a wide range of your science and engineering problems.
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations (PDEs) with parametric or uncertain inputs. In the algorithm, the stochastic Galerkin finite element method (sGFEM) is used to approximate the solutions to primal and dual problems that depend on a countably infinite number of uncertain parameters. Adaptive refinement is guided by an innovative strategy that combines the error reduction indicators computed for spatial and parametric components of the primal and dual solutions. The key theoretical ingredient is a novel two-level a posteriori estimate of the energy error in sGFEM approximations. We prove that this error estimate is reliable and efficient. The effectiveness of the goal-oriented error estimation strategy and the performance of the goal-oriented adaptive algorithm are tested numerically for three representative model problems with parametric coefficients and for three quantities of interest (including the approximation of pointwise values).
Goal-oriented dialogue systems typically rely on components specifically developed for a single task or domain. This limits such systems in two different ways: If there is an update in the task domain, the dialogue system usually needs to be updated or completely re-trained. It is also harder to extend such dialogue systems to different and multiple domains. The dialogue state tracker in conventional dialogue systems is one such component - it is usually designed to fit a well-defined application domain. For example, it is common for a state variable to be a categorical distribution over a manually-predefined set of entities (Henderson et al., 2013), resulting in an inflexible and hard-to-extend dialogue system. In this paper, we propose a new approach for dialogue state tracking that can generalize well over multiple domains without incorporating any domain-specific knowledge. Under this framework, discrete dialogue state variables are learned independently and the information of a predefined set of possible values for dialogue state variables is not required. Furthermore, it enables adding arbitrary dialogue context as features and allows for multiple values to be associated with a single state variable. These characteristics make it much easier to expand the dialogue state space. We evaluate our framework using the widely used dialogue state tracking challenge data set (DSTC2) and show that our framework yields competitive results with other state-of-the-art results despite incorporating little domain knowledge. We also show that this framework can benefit from widely available external resources such as pre-trained word embeddings.
The design of online algorithms has tended to focus on algorithms with worst-case guarantees, e.g., bounds on the competitive ratio. However, it is well-known that such algorithms are often overly pessimistic, performing sub-optimally on non-worst-case inputs. In this paper, we develop an approach for data-driven design of online algorithms that maintain near-optimal worst-case guarantees while also performing learning in order to perform well for typical inputs. Our approach is to identify policy classes that admit global worst-case guarantees, and then perform learning using historical data within the policy classes. We demonstrate the approach in the context of two classical problems, online knapsack and online set cover, proving competitive bounds for rich policy classes in each case. Additionally, we illustrate the practical implications via a case study on electric vehicle charging.
In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read performance being close to that of random access memory but writes being significantly more expensive in terms of energy and latency. We design algorithms for planar Delaunay triangulation, $k$-d trees, and static and dynamic augmented trees. Our algorithms are designed in the recently introduced Asymmetric Nested-Parallel Model, which captures the parallel setting in which there is a small symmetric memory where reads and writes are unit cost as well as a large asymmetric memory where writes are $omega$ times more expensive than reads. In designing these algorithms, we introduce several techniques for obtaining write-efficiency, including DAG tracing, prefix doubling, reconstruction-based rebalancing and $alpha$-labeling, which we believe will be useful for designing other parallel write-efficient algorithms.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
