Culturalismo y posmodernidad
4.1. La década de los cincuenta
Although some topics related to the MFS and the BEM were studied in the thesis, due to time limitations, some interesting problems can be considered in future research:
(1) Numerical evaluation of integrals with higher order singularities
In the present work on hypersingular integrals, the order of singularity is limited to two for line integrals and three for surface integrals. The developed regularisation process and the numerical treatment can be generalised to integrals with higher order singularities, provided that the complex-step derivative approach is able to approximate the derivatives of the density function for higher orders.
(2) Three-dimensional thermoelasticity caused by temperature changes in elastic media
The present MFS-CSRBF numerical scheme has seen applications to potential and elasticity problems. Multi-field problems such as thermoelasticity can also be solved by the MFS-CSRBF scheme, provided that the corresponding particular solution kernels of the multi-field problem are derived.
(3) Full implementation of meshed methods for porous media simulation
The present iteratively coupled solution scheme for simulating poroelasticity problems is implemented in the meshless method using MFS-CSRBF. However, this method tends to have stability issues for irregular or complex geometries as well as being sensitive to the locations of source points. Hence, potential improvements in computational efficiency and accuracy can be made by a full implementation of meshed method.
(4) Computational domain extends to surrounding bathing solution
The present computational domain for porous media simulation is limited to a single region, i.e. the material itself. In practice, a more comprehensive simulation would need to take into account the surrounding bathing solution, in which the porous media is
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immersed. This would require an understanding of the interface conditions across the material boundaries which could be examined in further research.
(5) Extend isotropy assumption to anisotropy
Throughout this thesis, isotropic elasticity and isotropic permeability assumptions are taken so as to simplify the solution finding processes, e.g. the derivation of CSRBF particular solution kernels, the respected fundamental solutions for the MFS, and the iteratively coupled solutions scheme for porous media simulation. Hence, extending the studies to anisotropy applications is highly desirable for future research projects.
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