Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 9 of 9 for “"layer potentials"”.
-
Mixed Problems and Layer Potentials for Harmonic and Biharmonic Functions
… solutions in terms of single and double layer potentials, establishing a mixed Rellich inequality, and applying functional analytic arguments to solve a two-by-two system of equations. These results are then extended to allow Robin data in place of Neumann data. This thesis also …
-
Layer potential evaluations on distributed memory machines
… partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the …
-
High-order numerical methods for layer potential evaluation
… of elliptic partial differential equations. Layer potentials play a central role in the integral equation formulation of boundary value problems. However, the numerical evaluation of layer potentials presents significant practical challenges associated with issues of singular/near-singular …
-
On finite element solutions for bounded time-harmonic scattering problems with an exact nonlocal boundary condition.
… exact nonlocal boundary condition utilizing layer potentials and Green's formulas, and we will explore both the Helmholtz and Maxwell equations with this setting. For the latter problem, we obtain a best-approximation result for the convergence rate as the mesh is refined. We will use …
-
Efficient high-order integral equation methods for the heat equation
… equations of the second kind via the heat layer potentials. Some advantages of the integral formulation as compared with standard finite difference and finite element methods include reduction of the dimension of the problem by one, high order accuracy, unconditional stability, …
-
Critical perturbations of elliptic operators by lower order terms
… p] spaces. Our approach is through the theory of layer potentials, though the lack of good estimates for solutions of L = 0 force us to use a more abstract construction of these objects, as opposed to the more classical definition through the fundamental solution. On the other hand, these more …
-
A Technique for Solving the Singular Integral Equations of Potential Theory
… in Electrostatics and Fracture Mechanics. Simple layer potential representations yield weakly singular integral equations for the induced charge on disc shaped conductors that are placed in an electrostatic field. Similarly, double layer potentials yield hyper-singular integral equations for the …
-
Articles on Potential Theory, Functional Analysis and Hankel Forms
… in J. Anal. Math., (2012). The boundary double layer potential, or the Neumann-Poincaré operator, is studied on the Sobolev space of order $1/2$ along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the whole space. Poincaré's …
-
Application of Extended DLVO Theory: Modeling of Flotation and Hydrophobicity of Dodecane
… parameters such as contact angle, double-layer potentials, particle size, bubble size, etc. The predictions were consistent with experience, and could be explained in view of the various subprocesses considered in the model development. Furthermore, the model suggested optimum conditions …