UoN / SACAMOS

Commit 2b58f1d5b75ebfeec7da21fced932ca1069cea56

Authored by Chris Smartt
1 parent efd7339e
Exists in master and in 3 other branches nested_overshields, proximity_effects, v4

minor updates to theory manual

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DOCUMENTATION/SACAMOS_TheoryManual.pdf
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DOCUMENTATION/THEORY_MANUAL/Tex/Laplace_Solver_Documentation.tex
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... ... @@ -110,7 +110,7 @@ Without an outer shield the electrostatic field is no longer confined to a bound
110 110  
111 111 %Of all available techniques we have chosen to truncate the domain by introducing a fictitious contour that encloses the domain of primary %interest and prescribe on it an asymptotic boundary condition which mimics the behaviour of the electrostatic potential in the region %outside the contour. Not only has it been shown that asymptotic boundaries give good results, the technique is relatively easy to implement %and preserves the sparsity of the finite element coefficient matrix which makes it a very efficient method as-well.\\
112 112  
113   -In unshielded condcutor configurations a suitable boundary condition must be applied on the outer boundary of the problems space. The imposition of a boundary condition will necessarily have an effect on the fields within the Finite Element domain and hence the capacitance matrix to be calculated. Three possible boundary conditions are outlined here, the Dirichelet boundary condition ($\phi=0$), the Neumann boundary condition $\frac{\partial \phi(r) }{\partial r}=0$ and an asymptotic boundary condition,
  113 +In unshielded conductor configurations a suitable boundary condition must be applied on the outer boundary of the problems space. The imposition of a boundary condition will necessarily have an effect on the fields within the Finite Element domain and hence the capacitance matrix to be calculated. Three possible boundary conditions are outlined here, the Dirichelet boundary condition ($\phi=0$), the Neumann boundary condition $\frac{\partial \phi(r) }{\partial r}=0$ and an asymptotic boundary condition,
114 114 $\frac{\partial \phi(r) }{\partial r}=\frac{1}{r ln(r)}\phi(r)$.
115 115  
116 116 \subsubsection{Dirichelet boundary conditions}
... ... @@ -127,7 +127,7 @@ This boundary condition enforces a condition that the normal derivitive of the p
127 127  
128 128 \subsubsection{Asymptotic boundary conditions}
129 129  
130   -For electrostatic problems, the potential in a point ${\bf{r}}$, can be written as\
  130 +For 2D electrostatic problems, the potential in a point ${\bf{r}}$, can be written as\
131 131 \\
132 132 \begin{equation}\phi\left(\mathbf{r}\right)=\iint_{\Omega}\rho\left(\mathbf{r}'\right) G\left(\mathbf{r},\mathbf{r}'\right)d\mathbf{r}'\end{equation}
133 133 \\
... ...