Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem

سال انتشار: 1398
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 418

فایل این مقاله در 15 صفحه با فرمت PDF قابل دریافت می باشد

استخراج به نرم افزارهای پژوهشی:

لینک ثابت به این مقاله:

شناسه ملی سند علمی:

JR_SCMA-15-1_004

تاریخ نمایه سازی: 22 مهر 1398

چکیده مقاله:

In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the Lax-Richtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method.

نویسندگان

Zahra Kalateh Bojdi

Department of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.

Ataollah Askari Hemmat

Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

Ali Tavakoli

Mathematics department, University of Mazandaran, Babolsar, Iran.

مراجع و منابع این مقاله:

لیست زیر مراجع و منابع استفاده شده در این مقاله را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود مقاله لینک شده اند :
  • G. Beylkin, Wavelets and Fast Numerical Algorithms, Lecture Notes for ...
  • G. Beylkin and N. Saito, Wavelets, their autocorrelation functions, and ...
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, and Th.A. Zang, Spectral ...
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, and Th.A. Zang, Spectral ...
  • G. Chen, Semi-analytical solutions for 2-D modeling of long pulsed ...
  • RJ. Chiffell, On the wave behavior and rate effect of ...
  • W. Dai, F. Han, and Z. Sun, Accurate Numerical Method ...
  • W. Dai and R. Nassar, A compact finite difference scheme ...
  • W. Dai and R. Nassar, A compact finite difference scheme ...
  • W. Dai and R. Nassar, A finite difference method for ...
  • W. Dai and R. Nassar, A finite difference scheme for ...
  • I. Daubechies, Ten Lectures on Wavelets, Soc. for Indtr. Appl. ...
  • J. Fan and L. Wang, Analytical theory of bioheat transport, ...
  • Z-Y. Guo and Y-S. Xu, Non-Fourier Heat Conduction in IC ...
  • Z. Kalateh Bojdi and A. Askari Hemmat, Wavelet collocation methods ...
  • Z. Kargar and H. Saeedi, B-spline wavelet operational method for ...
  • A. Latto, L. Resnikoff, and E. Tenenbaum, The evaluation of ...
  • A. Malek, Z. Kalateh Bojdi, and P. Nuri Niled Gobarg, ...
  • A. Malek and SH. Momeni-Masuleh, A Mixed Collocation-Finite Difference Method ...
  • A. Malek and S.H. Momeni-Masuleh, A Mixed Collocation-Finite Difference Method ...
  • S. Mallat, Multiresolution approximation and wavelets, Preprint GRASP Lab., Dept. ...
  • T.Q. Qui and C.L. Tien, Short-pulse laser heating on metals, ...
  • T.Q. Qui and C.L. Tien, Heat transfer mechanisms during short-pulse ...
  • G.D. Smith, Numerical Solution of Partial Differential Equations Finite Difference ...
  • D.Y. Tzou, Macro to Micro Heat Transfer, Washington, Taylor and ...
  • R. Viskanta and T.L. Bergman, Heat Transfer in Materials Processing, ...
  • D. Xue, Three-dimensional simulation of the temperature field in high-power ...
  • J. Zhang and J.J. Zhao, Iterative solution and finite difference ...
  • نمایش کامل مراجع