Document Type



Mechanical Engineering

First Advisor's Name

Igor Tsukanov

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Sabri Tosunoglu

Third Advisor's Name

Chunlei Wang


Meshfree, Engineering, Analysis, NanoStructures, Highgradient, ThinMaterials, EBFCAnalysis, BioFuelCell

Date of Defense



This study presents a numerical technique that enables exact treatment of all boundary conditions including those that are given on the interface boundary of two distinct media. This interface boundary conditions for Poisson equation are formulated as equality of the physical field and fluxes across the interface boundary. In this work first, the range of physical and geometric parameters which allow the applicability of the meshfree method with distance fields are tested and compared with analytical solution. Second, it investigates how the solution error depends on the ratio of B-spline support and thickness of the interface layer. Further, this study also concentrates on developing improved computational tools like 1D integration and modification of distance fields for analysis of diffusion concentration in heterogeneous material with high contrast of physical and geometrical properties. These improved computational tools for meshfree method with distance fields improve the accuracy of solution and decreases the computational time. Finally, these improved tools are used to solve a 2D problem for analysis of diffusion concentration and the results are compared to FEM solution to show that the improved tools yield computationally better results.