A PRACTICAL APPROACH TO FINITE‐DIFFERENCE RESISTIVITY MODELING

Geophysics ◽  
1978 ◽  
Vol 43 (5) ◽  
pp. 930-942 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Finite Difference ◽  
Point Source ◽  
Potential Field ◽  
Line Source ◽  
Sparse Matrix ◽  
Analytical Data ◽  
Parallel Layer ◽  
The Matrix ◽  
The Given ◽  
Resistivity Modeling

Highly efficient finite‐difference resistivity modeling algorithms which yield accurate results are put forward. The given medium is discretized and divided into rectangular blocks by using a very coarse system of vertical and horizontal grid lines, whose distance from the source(s) increases logarithmically. Expressions are derived to compute the longitudinal conductance and transverse resistance associated with each of these blocks for a parallel‐layer medium followed by a generalized treatment to accommodate arbitrarily shaped structures. Since the values of Dar Zarrouk parameters are derived from the exact resistivity distribution of the given medium, fine features such as a thin but anomalously resistive bed which ordinarily would be missed entirely in coarse discretization can be taken into account. Further reduction in the size of the model is achieved by making use of a symmetry wherever possible. In most cases the computation of the potential field which involves the inversion of a small sparse matrix requires about 0.5 sec of computer time. Moreover, changes in geology affect neither the size nor the zero structure of the matrix. Therefore, when more than one model is to be computed, the factorization of the matrix can be done symbolically only once for all models, followed by numeric factorization for each individual model. The coarse grid algorithm was applied to a number of horizontally layered models involving a point source. The results obtained for each model were in excellent agreement with the corresponding analytical data. Finite‐difference investigation of the potential field for two‐dimensional structures and a line source dipole indicates that as long as one is interested only in the evaluation of the Schlumberger‐type apparent resistivity curves, the line‐source results may be a much better approximation to the corresponding point‐source data than is commonly believed.

FINITE‐DIFFERENCE RESISTIVITY MODELING FOR ARBITRARILY SHAPED TWO‐DIMENSIONAL STRUCTURES

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 62-78 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Finite Difference ◽  
Potential Field ◽  
Line Source ◽  
Simulation Models ◽  
Iterative Solution ◽  
Single Step ◽  
Two Dimensions ◽  
Discrete Version ◽  
Grid Spacing ◽  
Source Dipole

Resistivity surveying is commonly done by using a point‐source dipole. Consequently, a finite‐difference evaluation of apparent resistivity curves implies the use of three‐dimensional simulation models which necessitate prohibitive computer costs. However, if we assume variation of resistivity only in two dimensions and use a line‐source dipole for setting up the finite‐difference model of a given structure, the potential field can be evaluated easily. A discrete version of the resistivity problem in two dimensions, which takes into account nonuniform grid spacing, is presented as a system of self‐adjoint difference equations. Since the iterative solution of such a system does not require grid spacing to be less than a certain critical value, it was successfully used for the development of fast‐convergence finite‐difference models. By examining in detail the characteristics of the matrix associated with the evaluation of the potential field, it is demonstrated that the proposed modeling procedure will remain stable for all conceivable geometries and resistivity distributions. It was used for the investigation of certain models for which the corresponding results could also be computed analytically. A direct superposition of results obtained in the two cases shows that they are virtually identical. By making use of the reciprocity theorem, a computational short‐cut, which provides the evaluation of vertical sounding curves for a line‐source dipole in a single step, is put forward. Special problems related to the optimization of acceleration parameters as well as the estimation of the potential function along the subsurface boundaries of the model are discussed. It is concluded that by surrounding the model by a termination strip of very large effective width, either Neumann‐ or Dirichlet‐type boundary conditions can be used for simulating a semiinfinite medium without introducing signficant errors in the results.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

Selecting optimal SpMV realizations for GPUs via machine learning

2021 ◽  
pp. 109434202199073
Author(s):  
Ernesto Dufrechou ◽  
Pablo Ezzatti ◽  
Enrique S Quintana-Ortí
Keyword(s):  
Machine Learning ◽  
Sparse Matrix ◽  
Machine Learning Techniques ◽  
Optimal Method ◽  
Learning Techniques ◽  
General Rules ◽  
Machine Learning Approach ◽  
The Matrix ◽  
Time And Energy ◽  
Matrix Vector

More than 10 years of research related to the development of efficient GPU routines for the sparse matrix-vector product (SpMV) have led to several realizations, each with its own strengths and weaknesses. In this work, we review some of the most relevant efforts on the subject, evaluate a few prominent routines that are publicly available using more than 3000 matrices from different applications, and apply machine learning techniques to anticipate which SpMV realization will perform best for each sparse matrix on a given parallel platform. Our numerical experiments confirm the methods offer such varied behaviors depending on the matrix structure that the identification of general rules to select the optimal method for a given matrix becomes extremely difficult, though some useful strategies (heuristics) can be defined. Using a machine learning approach, we show that it is possible to obtain unexpensive classifiers that predict the best method for a given sparse matrix with over 80% accuracy, demonstrating that this approach can deliver important reductions in both execution time and energy consumption.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

scholarly journals Integrated Recycling Process of Matrices of Organic Moulding Sands

2013 ◽  
Vol 58 (3) ◽  
pp. 809-812 ◽  
Author(s):  
R. Dańko
Keyword(s):  
Recycling Process ◽  
Conceptual Approach ◽  
Assessment Index ◽  
Experimental Stand ◽  
Synthetic Resins ◽  
The Matrix ◽  
Ignition Loss ◽  
On Line ◽  
The Given ◽  
Reclamation Process

Abstract The idea and experimental verification of assumptions of the integrated recycling process of matrices of uniform self-hardening moulding sands with synthetic resins, leading to obtaining moulding sands matrix of expected quality - is presented in the hereby paper. The basis of the presented process constitutes a combination of the method of forecasting averaged ignition losses of moulding sands after casting and defining the range of necessary matrix reclamation treatments in order to obtain its full recycling. Simultaneously, the empirically determined dependence of dusts amounts emitted during the reclamation process of the matrix from the given spent sand on the ignition loss values (which is the most proper assessment index of the obtained reclaimed material quality) was taken into account. The special experimental stand for investigations of the matrix recycling process was one of the elements of the conceptual approach and verification of its assumptions. The stand was equipped with the system of current on-line control of the purification degree of matrix grains from organic binder remains. The results of own investigations, allowing to combine ignition loss values of spent moulding sands after casting knocking out with amounts of dusts generated during the mechanical reclamation treatment of such sands, were utilized in the system.

scholarly journals Fast and Robust Orientation of Cryo-Electron Microscopy Images

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Guoliang Xu ◽  
Xia Wang ◽  
Ming Li ◽  
Zhucui Jing
Keyword(s):  
Sparse Matrix ◽  
Three Dimensional ◽  
Image Plane ◽  
Real Space ◽  
Computation Method ◽  
Common Line ◽  
The Matrix ◽  
Common Lines ◽  
The Common ◽  
Dimensional Object

AbstractWe present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.

scholarly journals State estimation for bilinear impulsive control systems under uncertainties

2018 ◽  
pp. 35-41 ◽  
Author(s):  
Oxana G. Matviychuk
Keyword(s):  
Differential Equations ◽  
State Estimation ◽  
Control Systems ◽  
Uncertain Systems ◽  
Impulsive Control ◽  
Compact Set ◽  
The Matrix ◽  
Initial States ◽  
Impulsive Control Systems ◽  
The Given

The state estimation problem for uncertain impulsive control systems with a special structure is considered. The initial states are taken to be unknown but bounded with given bounds. We assume here that the coefficients of the matrix included in the differential equations are not exactly known, but belong to the given compact set in the corresponding space. We present here algorithms that allow to find the external ellipsoidal estimates of reachable sets for such bilinear impulsive uncertain systems.

scholarly journals Transformation of land use pattern in the East Borsod coal basin from the beginning of minig industry to the political changes

2016 ◽  
Vol 10 (3-4) ◽  
pp. 223-231
Author(s):  
László Sütő ◽  
Erika Homoki ◽  
Zoltán Dobány ◽  
Péter Rózsa
Keyword(s):  
Land Cover ◽  
Human Disturbance ◽  
The Political ◽  
Early 20Th Century ◽  
Late Period ◽  
Topographic Map ◽  
Coal Basin ◽  
Land Use Pattern ◽  
The Matrix ◽  
The Given

Historical geographic studies on land cover may support the understanding of the recent state. Focusing on coal mining, this process was followed and analyzed in the case of the East Borsod Coal Basin from the early 20th century to the political change. The contemporaneous maps and manuscripts concerning the mining were evaluated using geoinformatic techniques. Moreover, digitalized topographic map coming from the early and late period of mining (1924 and 1989, respectively) were analyzed. To determine the degree of human disturbance hemerobic relations and changes of the given land cover patches were quantified on the basis of the maps of the three military surveys, too. It can be stated that montanogenic subtype of an industrialagricultural landscape has been formed in the Bükkhát area. Beside the concentrated artificial surfaces, however, relative dominance of forest forming the matrix of the landscape remained.

scholarly journals ВДОСКОНАЛЕНА ПОЛІНОМІАЛЬНО-СКЛАДНА АТАКА ВІДНОВЛЕННЯ ВІДКРИТОГО ТЕКСТУ НА РАНЦЕВИЙ ШИФР НА ОСНОВІ МАТРИЦЬ

2020 ◽  
pp. 67-74
Author(s):  
Олексій Сергійович Вамболь
Keyword(s):  
Discrete Logarithm ◽  
Public Information ◽  
Galois Field ◽  
Secret Key ◽  
The Matrix ◽  
Encryption Schemes ◽  
Shared Secret ◽  
Symmetric Key ◽  
Asymmetric Encryption ◽  
The Given

Asymmetric ciphers are widely used to ensure the confidentiality of data transmission via insecure channels. These cryptosystems allow the interacting parties to create a shared secret key for a symmetric cipher in such a way that an eavesdropper gets no information useful for cryptanalysis. Network security protocols that use asymmetric ciphers include TLS, S/MIME, OpenPGP, Tor, and many others. Some of the asymmetric encryption schemes are homomorphic, that is, that they allow calculations on encrypted data to be performed without preliminary decryption. The aforesaid property makes possible using these cryptosystems not only for symmetric key establishment but also in several areas of application, in particular in secret voting protocols and cloud computing. The matrix-based knapsack cipher is a new additively homomorphic asymmetric encryption scheme, which is based on the properties of isomorphic transformations of the inner direct product of diagonal subgroups of a general linear group over a Galois field. Unlike classic knapsack encryption schemes, the cryptographic strength of this cipher depends on the computational complexity of the multidimensional discrete logarithm problem. Despite some useful properties, further research into the cryptographic strength of the matrix-based knapsack cipher has found serious drawbacks inherent in this cryptographic scheme. In the given paper an improved polynomial-time plaintext-recovery attack on the matrix-based knapsack cipher is proposed. Applying this cryptanalytic method requires only public information and has time complexity O(t1.34), where t denotes the decryption time of the attacked cryptosystem. The aforementioned attack is more productive and easier to implement in software in comparison with the original one. The advantages of the proposed method are due to using in its algorithm the simple and relatively fast matrix trace operation instead of more complex and slower transformations.

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