Examinando por Autor "Millwater, Harry"

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    Quaternion and octonion-based finite element analysis methods for computing multiple first order derivatives
    (Elsevier Inc., 2019-11-15) Aristizabal, Mauricio; Ramirez-Tamayo, Daniel; Garcia, Manuel; Aguirre-Mesa, Andres; Montoya, Arturo; Millwater, Harry; Mecánica Aplicada
    The complex Taylor series expansion method for computing accurate first order derivatives is extended in this work to quaternion, octonion and any order Cayley-Dickson algebra. The advantage of this new approach is that highly accurate multiple first order derivatives can be obtained in a single analysis. Quaternion and octonion-based finite element analysis methods were developed in order to compute up to three (quaternion) and up to seven (octonion) first order derivatives of shape, material properties, and/or loading conditions in a single analysis. The traditional finite element formulation was modified such that each degree-of-freedom was augmented with three or seven additional imaginary nodes. The quaternion and octonion-based methods were integrated within the Abaqus commercial finite element code through a user element subroutine. Numerical examples are presented for thermal conductivity and linear elasticity; however, the methodology is general. The results indicate that the quaternion and octonion-based methods provide derivatives of the same high accuracy as the complex finite element method but are significantly more efficient. A Fortran code to solve a simple seven variable quaternion example is given in the Appendix. (C) 2019 Elsevier Inc. All rights reserved.
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    Sensitivity analysis for radiofrequency induced thermal therapies using the complex finite element method
    (ELSEVIER SCIENCE BV, 2017-11-01) Monsalvo, Juan F.; Garcia, Manuel J.; Millwater, Harry; Feng, Yusheng; Mecánica Aplicada
    In radiofrequency induced thermal procedures for cancer treatment, the temperature of the cancerous tissue is raised over therapeutic values while maintaining the temperature of the surrounding tissue at normal levels. In order to control these temperature levels during a thermal therapy, it is important to predict the temperature distribution over the region of interest and analyze how the variations of the different parameters can affect the temperature in the healthy and damaged tissue. This paper proposes a sensitivity analysis of the radiofrequency induced thermal procedures using the complex Taylor series expansion (CTSE) finite element method (ZFEM), which is more accurate and robust compared to the finite difference method. The radiofrequency induced thermal procedure is modeled by the bioheat and the Joule heating equations. Both equations are coupled and solved using complex-variable finite element analysis. As a result, the temperature sensitivity with respect to any material property or boundary condition involved in the process can be calculated using CTSE. Two thermal therapeutical examples, hyperthermia and ablation induced by radio frequency, are presented to illustrate the capabilities and accuracy of the method. Relative sensitivities of the temperature were computed for a broad range of parameters involved in the radiofrequency induced thermal process using ZFEM. The major feature of the method is that it enables a comprehensive evaluation of the problem sensitivities, including both model parameters and boundary conditions. The accuracy and efficiency of the method was shown to be superior to the finite difference method. The computing time of a complex finite element analysis is about 1.6 times the computing time of real finite element analysis; significantly lower than the 2 times of forward/backward finite differencing or 3 times of central differencing. It was found that the radiofrequency hyperthermia procedure is very sensitive to the electric field and temperature boundary conditions. In the case of the radiofrequency ablation procedure, the cooling temperature of the electrodes has the highest liver/tumor temperature sensitivity. Also, thermal and electrical conductivities of the healthy tissue were the properties with the highest temperature sensitivities. The result of the sensitive analysis can be used to design very robust and safe medical procedures as well as to plan specific patient procedures.