Lecture 4. - Revision history

Marcsa: /* Equation Options */

2020-04-01T13:38:35Z

‎Equation Options

Marcsa: Undo revision 1889 by Marcsa (talk)

2020-03-31T08:41:18Z

Undo revision 1889 by Marcsa (talk)

Marcsa: /* Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM) */

2020-03-31T08:39:49Z

‎Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM)

Marcsa: /* Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM) */

2020-03-31T08:27:03Z

‎Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM)

Marcsa: /* Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM) */

2020-03-31T07:46:33Z

‎Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM)

Marcsa: /* Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM) */

2020-03-31T07:46:07Z

‎Method of Moments (MoM)CVEL - Electromagnetic Modeling (MoM)

Marcsa: /* Boundary Element Method (BEM)CVEL - Electromagnetic Modeling (BEM) */

2020-03-30T09:49:36Z

‎Boundary Element Method (BEM)CVEL - Electromagnetic Modeling (BEM)

Marcsa: /* Boundary Element Method (BEM)CVEL - Electromagnetic Modeling (BEM) */

2020-03-30T09:47:55Z

‎Boundary Element Method (BEM)CVEL - Electromagnetic Modeling (BEM)

Marcsa: /* Wave EquationsD. M. Pozar - Microwave Engineering, John Wiley & Sons. Inc., 2012. */

2020-03-29T14:55:39Z

‎Wave EquationsD. M. Pozar - Microwave Engineering, John Wiley & Sons. Inc., 2012.

Marcsa: /* Boundary Element Method (BEM)CVEL - Electromagnetic Modeling (BEM) */

2020-03-29T14:55:26Z

‎Boundary Element Method (BEM)CVEL - Electromagnetic Modeling (BEM)

@@ Line 134: / Line 134: @@
 Moment Method codes based on the EFIE or MFIE alone, may exhibit unstable behavior when the modeling surfaces form a resonant cavity at a particular frequency. To avoid this, many moment method codes solve a linear combination of the EFIE and MFIE known as a ''Combined Field Integral Equation'' (CFIE). This requires more calculations to fill the matrix, but results in a more stable solution when the modeling surface is large enough to support an interior resonance.
-Some CEM modeling codes employ the Method of Moments to solve other equations. For example, static modeling codes often solve a form of Laplace's equation relating electric field strengths to charge densities or magnetic field strengths to current densities. The Generalized Multiple Technique (GMT), which is described in another section of this report, employs a moment method to solve equations for the electric field generated by multipole sources.
+Some CEM modeling codes employ the Method of Moments to solve other equations. For example, static modeling codes often solve a form of Laplace's equation relating electric field strengths to charge densities or magnetic field strengths to current densities. The Generalized Multipole Technique (GMT) employs a moment method to solve equations for the electric field generated by multipole sources.
 ==== Basis and Weighting Function ====

@@ Line 73: / Line 73: @@
 <blockquote>
-Már 1960-ban, mások mellett R.F. Harrington is alkalmazott egy ''momentumok módszerének'' nevezett eljárást elektromágneses feladatok megoldására. A momentumok módszere egy eljárás ami a feladatotot lineáris egyenletrenszerré képezi le
+In the 1960s, R.F. Harrington and others applied a technique called the ''Method of Moments'' to the solution of electromagnetic field problems. The Method of Moments (also called the Method of Weighted Residuals) is a technique for solving linear equations of the form,
 ::<math>\mathcal{L}(\phi)=f</math>
-ahol a <math>\mathcal{L}(\bullet)</math> funkcionál egy lineáris operátor, az <math>f</math> az ismert gerjesztés vagy kényszer függvénye és a <math>\phi</math> az ismeretlen mennyiség. Ahhoz, hogy számítógépen kezelhető feladatot kapjunk, a feladatot <math>N</math> részre (2D - vonal, 3D - felület) felbontjuk, majd az ismeretlen függvényt ugyanennyi súlyozott bázisfüggvény (<math>v_n</math>) összegeként kell közelíteni,
+where the functional <math>\mathcal{L}(\bullet)</math> is a linear operator, <math>f</math> is a known excitation or forcing function, and <math>\phi</math> is an unknown quantity. To solve this problem on a digital computer, we start by expressing the unknown solution as a series of basis or expansion functions, <math>v_n</math>,
 ::<math>\phi = \sum_{n=1}^{N}a_n v_n</math>
-ahol <math>a_n</math> az ismeretlen együttható, ami a sorozat egyes tagjainak az amplitúdóját adja meg.
+where <math>a_n</math> are unknown coefficients describing the amplitude of each term in the series.
-Ennek következtében, most nem egy egyenletünk van a <math>\phi</math> ismeretlennel, hanem ehelyett <math>N</math> darab skalár ismeretlen van,
+Now instead of one equation with a continuous unknown quantity, <math>\phi</math>, we have an equation with <math>N</math> scalar unknowns,
 ::<math>\mathcal{L}(a_1v_1+a_2v_2+\dots+a_Nv_N)=f</math>.
-Ahhoz, hogy meghatározzuk <math>a_n</math> értékeit, <math>N</math> darab egymástól lineárisan független egyenletre van szüségünk; amihez <math>a_n</math> különböző súly- vagy tesztfüggvényeket, <math>w_n</math>-t alkalmazunk. Ennek következtében <math>N</math> egyenletből álló egyenletrendszerünk van az<math>N</math> ismeretlenhez:
+To solve for the values of <math>a_n</math>, we need <math>N</math> linearly independent equations; so <math>a_n</math> different weighting or testing functions, <math>w_n</math>, are applied. This yields the following system of <math>N</math> equations in <math>N</math> unknowns:
 ::<math>
@@ Line 110: / Line 110: @@
 </math>
-A fenti összefüggés lineáris egyenletrendszerként a következő lesz
+This linear system of equations has the form,
 ::<math>\textbf{A}\textbf{x}=\textbf{b}</math>

@@ Line 73: / Line 73: @@
 <blockquote>
-In the 1960s, R.F. Harrington and others applied a technique called the ''Method of Moments'' to the solution of electromagnetic field problems. The Method of Moments (also called the Method of Weighted Residuals) is a technique for solving linear equations of the form,
+Már 1960-ban, mások mellett R.F. Harrington is alkalmazott egy ''momentumok módszerének'' nevezett eljárást elektromágneses feladatok megoldására. A momentumok módszere egy eljárás ami a feladatotot lineáris egyenletrenszerré képezi le
 ::<math>\mathcal{L}(\phi)=f</math>
-where the functional <math>\mathcal{L}(\bullet)</math> is a linear operator, <math>f</math> is a known excitation or forcing function, and <math>\phi</math> is an unknown quantity. To solve this problem on a digital computer, we start by expressing the unknown solution as a series of basis or expansion functions, <math>v_n</math>,
+ahol a <math>\mathcal{L}(\bullet)</math> funkcionál egy lineáris operátor, az <math>f</math> az ismert gerjesztés vagy kényszer függvénye és a <math>\phi</math> az ismeretlen mennyiség. Ahhoz, hogy számítógépen kezelhető feladatot kapjunk, a feladatot <math>N</math> részre (2D - vonal, 3D - felület) felbontjuk, majd az ismeretlen függvényt ugyanennyi súlyozott bázisfüggvény (<math>v_n</math>) összegeként kell közelíteni,
 ::<math>\phi = \sum_{n=1}^{N}a_n v_n</math>
-where <math>a_n</math> are unknown coefficients describing the amplitude of each term in the series.
+ahol <math>a_n</math> az ismeretlen együttható, ami a sorozat egyes tagjainak az amplitúdóját adja meg.
-Now instead of one equation with a continuous unknown quantity, <math>\phi</math>, we have an equation with <math>N</math> scalar unknowns,
+Ennek következtében, most nem egy egyenletünk van a <math>\phi</math> ismeretlennel, hanem ehelyett <math>N</math> darab skalár ismeretlen van,
 ::<math>\mathcal{L}(a_1v_1+a_2v_2+\dots+a_Nv_N)=f</math>.
-To solve for the values of <math>a_n</math>, we need <math>N</math> linearly independent equations; so <math>a_n</math> different weighting or testing functions, <math>w_n</math>, are applied. This yields the following system of <math>N</math> equations in <math>N</math> unknowns:
+Ahhoz, hogy meghatározzuk <math>a_n</math> értékeit, <math>N</math> darab egymástól lineárisan független egyenletre van szüségünk; amihez <math>a_n</math> különböző súly- vagy tesztfüggvényeket, <math>w_n</math>-t alkalmazunk. Ennek következtében <math>N</math> egyenletből álló egyenletrendszerünk van az<math>N</math> ismeretlenhez:
 ::<math>
@@ Line 110: / Line 110: @@
 </math>
-This linear system of equations has the form,
+A fenti összefüggés lineáris egyenletrendszerként a következő lesz
 ::<math>\textbf{A}\textbf{x}=\textbf{b}</math>

@@ Line 83: / Line 83: @@
 where <math>a_n</math> are unknown coefficients describing the amplitude of each term in the series.
-Now instead of one equation with a continuous unknown quantity, <math>f</math>, we have an equation with <math>N</math> scalar unknowns,
+Now instead of one equation with a continuous unknown quantity, <math>\phi</math>, we have an equation with <math>N</math> scalar unknowns,
 ::<math>\mathcal{L}(a_1v_1+a_2v_2+\dots+a_Nv_N)=f</math>.

@@ Line 73: / Line 73: @@
 <blockquote>
-In the 1960s, R.F. Harrington<ref>[https://ieeexplore.ieee.org/book/5264717 R. F. Harrington - Time Harmonic Electromagnetic Fields, New York, McGraw Hill, 1961.]</ref> and others applied a technique called the ''Method of Moments'' to the solution of electromagnetic field problems. The Method of Moments (also called the Method of Weighted Residuals) is a technique for solving linear equations of the form,
+In the 1960s, R.F. Harrington and others applied a technique called the ''Method of Moments'' to the solution of electromagnetic field problems. The Method of Moments (also called the Method of Weighted Residuals) is a technique for solving linear equations of the form,
 ::<math>\mathcal{L}(\phi)=f</math>

@@ Line 59: / Line 59: @@
 |-
+|
-* Excels at modeling inhomogeneous or complex materials
+* Excellent for modeling unbounded (radiation) problems.
-* Excels at modeling problems that combine small detailed geometries with larger objects
+* Excellent for modeling metal plates and thin wires.
-* Excels at modeling structures in resonant cavities or waveguides
+* Good for modeling structures with lumped circuit elements included.
+|
-* Absorbing boundary required for modeling unbounded (radiation) problems
+* Does not model inhomogeneous or complex materials well.
-* Difficult to model thin/electrically large or resonant wires accurately
+* Not good for modeling problems that combine small detailed geometries with larger objects.
 |}

← Older revision		Revision as of 09:47, 30 March 2020
Line 52:		Line 52:

	Following table lists various strengths and weakness of BEM modeling techniques. Note that the capabilities of any particular modeling software depend strongly on the form of the integral equation solved, the choice of basis and weighting functions, the Green's function(s) employed, and the matrix solver and any optimization techniques employed.		Following table lists various strengths and weakness of BEM modeling techniques. Note that the capabilities of any particular modeling software depend strongly on the form of the integral equation solved, the choice of basis and weighting functions, the Green's function(s) employed, and the matrix solver and any optimization techniques employed.
		+
		+	{\| class="wikitable"
		+	\|-
		+	! Strengths
		+	! Weaknesses
		+	\|-
		+	\|
		+	* Excels at modeling inhomogeneous or complex materials
		+	* Excels at modeling problems that combine small detailed geometries with larger objects
		+	* Excels at modeling structures in resonant cavities or waveguides
		+	\|
		+	* Absorbing boundary required for modeling unbounded (radiation) problems
		+	* Difficult to model thin/electrically large or resonant wires accurately
		+	\|}

	</blockquote>		</blockquote>

@@ Line 130: / Line 130: @@
 == Wave Equations<ref>[https://www.wiley.com/en-us/Microwave+Engineering%2C+4th+Edition-p-9780470631553 D. M. Pozar - Microwave Engineering, John Wiley & Sons. Inc., 2012.]</ref> ==
 <blockquote>
-We will deal with the tim-harmonic case directly in terms of the electric and magnetic fields. For this, it is necessary to derive from Maxwell's equations, which involve both electric and magnetic fields, the governing differential equations involving only either field.
+We will deal with the time-harmonic case directly in terms of the electric and magnetic fields. For this, it is necessary to derive from Maxwell's equations, which involve both electric and magnetic fields, the governing differential equations involving only either field.
 === Vector Wave Equations ===

@@ Line 35: / Line 35: @@
 Equations below show a common form of the EFIE and MFIE employed by boundary element method codes that model metallic objects only (i.e. there are no equivalent magnetic surface currents);
-::<math>\vec{E}(\vec{r})=\frac{-j\eta}{4\pi k}\int_S\vec{J}_S(\vec{r}')\cdot\vec{G}_e(\vec{r},\vec{r}')\text{d}S'</math>
+::<math>\vec{E}(\vec{r})=\frac{-j\eta}{4\pi k}\int_S\vec{J}_S(\vec{r}')\cdot\vec{G}_e(\vec{r},\vec{r}')\text{d}S'</math>;
-::<math>\vec{H}(\vec{r})=\frac{1}{4\pi}\int_S\vec{J}_S(\vec{r}')\times\nabla'\vec{G}_m(\vec{r},\vec{r}')\text{d}S'</math>
+::<math>\vec{H}(\vec{r})=\frac{1}{4\pi}\int_S\vec{J}_S(\vec{r}')\times\nabla'\vec{G}_m(\vec{r},\vec{r}')\text{d}S'</math>.
 In these equations, <math>\int_S \text{d}S'</math> integral over the surface represents integration over all boundary surfaces. Note that since the boundary only exists at places where an interface between two different materials occurred, the size of the boundary is limited (i.e. there is no integration to infinity).