Overview of adaptive and low-rank approximation algorithms for modeling influence of electromagnetic waves generated by cellphone antenna on human head

• Autorzy: Głut Barbara , Paszyński Maciej

Identyfikatory

DOI

10.7494/csci.2021.22.4.4251

• Języki publikacji: EN

Abstrakty

EN

This paper presents an overview of formulations and algorithms that are dedicated to modeling the influence of electromagnetic waves on the human head. We start from h adaptive approximation of a three-dimensional MRI scan of the human head. Next, we solve the time-harmonic Maxwell equations with a 1.8 GHz cellphone antenna. We compute the specific absorption rate used as the heat source for the Pennes bioheat equation modeling the heat generated by EM waves inside the head. We propose an adaptive algorithm mixed with time-stepping iterations where we simultaneously refine the computational mesh, solve the Maxwell and Pennes equations, and iterate the time steps. We employ the sparse Gaussian elimination algorithm with the low-rank compres-sion of the off-diagonal matrix blocks for the factorization of the matrices. We conclude with the statement that 15 minutes of talking with a 1.8 GHz antenna with one watt of power results in increased brain tissue temperatures (up to 38.4◦C).

Słowa kluczowe

EN

mesh generation; mesh adaptation; Pennes bioheat equations; time-harmonic Maxwell equations; sparse factorization; low rank approximation

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2021
• Tom: T. 22 (4)
• Strony: 433--461
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Głut Barbara

• AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland

autor

Paszyński Maciej

• AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

• [1] Albers B., Savidis S., Tasan H.E., von Estorff O., Gehlken M.: BEM and FEM results of displacements in a poroelastic column, International Journal of Applied Mathematics and Computer Science, vol. 22(4), pp. 883–896, 2012.
• [2] Amestoy P.R., Buttari A., L’Excellent J.Y., Mary T.: Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures, ACM Transactions on Mathematical Software, vol. 45(1), pp. 1–26, 2019.doi: 10.1145/3242094.
• [3] Demkowicz L.: Computing with hp-ADAPTIVE FINITE ELEMENTS, Vol.I. One and Two Dimensional Elliptic and Maxwell Problems, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science, 2006.
• [4] Demkowicz L., Kurtz J., Pardo D., Paszy ́nski M., Rachowicz W., Zdunek A.: Computing with hp-ADAPTIVE FINITE ELEMENTS, Vol. II. Frontiers. ThreeDimensional Elliptic and Maxwell Problems with Applications, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science, 2007.
• [5] Duff I.S., Reid J.K.: The Multifrontal Solution of Indefinite Sparse Symmetric Linear, ACM Transactions on Mathematical Software, vol. 9(3), pp. 302–325, 1983.
• [6] Duff I.S., Reid J.K.: The Multifrontal Solution of Unsymmetric Sets of Linear Equations, Journal on Scientific and Statistical Computing, vol. 5, pp. 633–641 1984.
• [7] Forouharmajd F., Ebrahimi H., Pourabdian S.: Mobile Phone Distance From Head and Temperature Changes of Radio Frequency Waves on Brain Tissue, International Journal of Preventive Medicine, vol. 9(1), p. 61, 2018. doi: 10.4103/ijpvm.IJPVM 70 17.
• [8] Garcia-Castillo L., Gomez-Revuelto I., Amor-Martin A., Łoś M., Paszyński M.: Algorithm for simultaneous adaptation and time step iterations for the electromagnetic waves propagation and heating of the human head induced by cell phone, Procedia Computer Science, vol. 108, pp. 2448–2452, 2017.
• [9] Garcia-Dooro D.: A new software suite for electromagnetics, Ph.D. thesis, Universidad Carlos III de Madrid, 2014.
• [10] Geng P., Oden T.J., van de Geijn R.A.: A parallel multifrontal algorithm and its implementation, Computer Methods in Applied Mechanics and Engineering, vol. 149(1–4), pp. 289–301, 1997. doi: 10.1016/S0045-7825(97)00052-2.
• [11] Hughues T.J.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Civil and Mechanical Engineering, 2000.
• [12] Iqbal-Faruque M., Aisyah-Husni N., Ikbal-Hossain M., Tariqul-Islam M., Misran N.: Effects of Mobile Phone Radiation onto Human Head with Variation of Holding Cheek and Tilt Positions, Journal of Applied Research and Technology, vol. 12(5), pp. 871–876, 2014. doi: 10.1016/S1665-6423(14)70593-0.
• [13] Jeannerod C.P., Mary T., Pernet C., Roche D.S.: Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic, SIAM Journal on Matrix Analysis and Applications, vol. 40(4), pp. 1478–1496, 2019. doi: 10.1137/19M1255628.
• [14] Kyunogjoo K.: Finite element modeling of the radiation and induced heat transfer in the human body, Ph.D. thesis, The University of Texas at Austin, 2013.
• [15] Michler C., Demkowicz L., Kurtz J., Pardo D.: Improving the performance of perfectly matched layers by means of hp-adaptivity, Numerical Methods for Partial Differential Equations, vol. 23(4), pp. 832–858, 2007. doi: 10.1002/num.20252.
• [16] Paszyński M.: Fast Solvers for Mesh Based Computations, Taylor & Francis, CRC Press, 2016.
• [17] Pilat A.: FEMLab software applied to Active Magnetic Bearing analysis, International Journal of Applied Mathematics and Computer Science, vol. 14(4), pp. 497–501, 2004.
• [18] Salazar-Palma M., Sarkar T.K., Garcia-Castillo L.E., Roy T., Djordjevic A.R.: Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Artech House Publishers, 1998.
• [19] Schaefer R., Łoś M., Sieniek M., Demkowicz L., Paszyński M.: Quasi-linear computational cost adaptive solvers for three dimensional modeling of heating of a human head induced by cell phone, Journal of Computational Science, vol. 11, pp. 163–174, 2015.
• [20] Stanković V., Jovanović D., Krsti ́c D., Markovi ́c V., Cvetkovi ́c N.: Temperature distribution and Specific Absorption Rate inside a child’s head, International Journal of Heat and Mass Transfer, vol. 104, pp. 559–565, 2017. doi: 10.1016/j.ijheatmasstransfer.2016.08.094