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Special Issue "Computing Methods in Mathematics and Engineering"

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (20 February 2022) | Viewed by 4534

Special Issue Editor

Prof. Dr. Chong Wang
E-Mail Website
Guest Editor
Institute of Solid Mechanics, Beihang University, Beijing 100191, China
Interests: uncertainty analysis and optimization; interval and fuzzy theory; parameter identification; model verification and validation

Special Issue Information

Dear Colleagues,

With the rapid development of modern computer technology, computing methods play an increasingly important role in solving various scientific and engineering problems. This rapid development is accomplished through novel mathematical modeling and advanced numerical computing, which reflects a combination of concepts, methods and principles in multi-scale, multi-physics, or multi-disciplinary problems.

This Special Issue will be a platform for the papers with novelty in computational mathematics and engineering, also providing an opportunity for researchers and practitioners to discuss the theoretical development and rational applications of computing methods in the analysis and design of engineering systems. Contributions in a wide range of areas are welcome, including but not limited to the computational issues about model reduction, uncertainty quantification, response prediction, optimization design, parameter identification, and machine learning in the following engineering fields:

  • Mechanical manufacture
  • Aeronautics and astronautics
  • Materials science and engineering
  • Electrification and automation
  • Structural mechanics
  • Electromagnetics
  • Civil engineering

Prof. Dr. Chong Wang
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mathematical modeling
  • Computing methods
  • Complex engineering systems
  • Multi-disciplinary
  • Uncertainty quantification
  • Optimization design
  • Machine learning

Published Papers (3 papers)

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Research

Article
Reliability-Based Design Optimization of Structures Considering Uncertainties of Earthquakes Based on Efficient Gaussian Process Regression Metamodeling
Axioms 2022, 11(2), 81; https://doi.org/10.3390/axioms11020081 - 20 Feb 2022
Cited by 1 | Viewed by 904
Abstract
The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under [...] Read more.
The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under stochastic earthquakes based on adaptive Gaussian process regression (GPR) metamodeling is proposed in this study. In this method, the uncertainties of ground motions are described by the record-to-record variation and the randomness of intensity measure (IM). A GPR model is constructed to obtain the approximations of the engineering demand parameter (EDP), and an active learning (AL) strategy is presented to adaptively update the design of experiments (DoE) of this metamodel. Based on the reliability of design variables calculated by Monte Carlo simulation (MCS), an optimal solution can be obtained by an efficient global optimization (EGO) algorithm. To validate the effectiveness and efficiency of the developed method, it is applied to the optimization problems of a steel frame and a reinforced concrete frame and compared with the existing methods. The results show that this method can provide accurate reliability information for seismic design and can deal with the problems of minimizing costs under the probabilistic constraint and problems of improving the seismic reliability under limited costs. Full article
(This article belongs to the Special Issue Computing Methods in Mathematics and Engineering)
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Article
Zero-Aware Low-Precision RNS Scaling Scheme
Axioms 2022, 11(1), 5; https://doi.org/10.3390/axioms11010005 - 23 Dec 2021
Viewed by 1409
Abstract
Scaling is one of the complex operations in the Residue Number System (RNS). This operation is necessary for RNS-based implementations of deep neural networks (DNNs) to prevent overflow. However, the state-of-the-art RNS scalers for special moduli sets consider the 2k modulo as [...] Read more.
Scaling is one of the complex operations in the Residue Number System (RNS). This operation is necessary for RNS-based implementations of deep neural networks (DNNs) to prevent overflow. However, the state-of-the-art RNS scalers for special moduli sets consider the 2k modulo as the scaling factor, which results in a high-precision output with a high area and delay. Therefore, low-precision scaling based on multi-moduli scaling factors should be used to improve performance. However, low-precision scaling for numbers less than the scale factor results in zero output, which makes the subsequent operation result faulty. This paper first presents the formulation and hardware architecture of low-precision RNS scaling for four-moduli sets using new Chinese remainder theorem 2 (New CRT-II) based on a two-moduli scaling factor. Next, the low-precision scaler circuits are reused to achieve a high-precision scaler with the minimum overhead. Therefore, the proposed scaler can detect the zero output after low-precision scaling and then transform low-precision scaled residues to high precision to prevent zero output when the input number is not zero. Full article
(This article belongs to the Special Issue Computing Methods in Mathematics and Engineering)
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Article
The Representation of D-Invariant Polynomial Subspaces Based on Symmetric Cartesian Tensors
Axioms 2021, 10(3), 193; https://doi.org/10.3390/axioms10030193 - 19 Aug 2021
Cited by 1 | Viewed by 763
Abstract
Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of the D-invariant (closed under differentiation) polynomial subspaces has significant meaning for multivariate Hermite-type interpolation (especially ideal interpolation). We analyze the structure of a D [...] Read more.
Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of the D-invariant (closed under differentiation) polynomial subspaces has significant meaning for multivariate Hermite-type interpolation (especially ideal interpolation). We analyze the structure of a D-invariant polynomial subspace Pn in terms of Cartesian tensors, where Pn is a subspace with a maximal total degree equal to n,n1. For an arbitrary homogeneous polynomial p(k) of total degree k in Pn, p(k) can be rewritten as the inner products of a kth order symmetric Cartesian tensor and k column vectors of indeterminates. We show that p(k) can be determined by all polynomials of a total degree one in Pn. Namely, if we treat all linear polynomials on the basis of Pn as a column vector, then this vector can be written as a product of a coefficient matrix A(1) and a column vector of indeterminates; our main result shows that the kth order symmetric Cartesian tensor corresponds to p(k) is a product of some so-called relational matrices and A(1). Full article
(This article belongs to the Special Issue Computing Methods in Mathematics and Engineering)
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