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# Computational Electromagnetics ECEN 5154

GPA 3.9

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This 2 page Study Guide was uploaded by Mrs. Lacy Schneider on Thursday October 29, 2015. The Study Guide belongs to ECEN 5154 at University of Colorado at Boulder taught by Dejan Filipovic in Fall. Since its upload, it has received 55 views. For similar materials see /class/231783/ecen-5154-university-of-colorado-at-boulder in ELECTRICAL AND COMPUTER ENGINEERING at University of Colorado at Boulder.

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Date Created: 10/29/15

Equot JRW U 00gt 0 O N W 4 Study questions for the ECEN5154 a 30min quiz February 15 2007 How would you classify the boundary value problems that arise in EM Provide a brief description for all categories What is the difference between open and closed domain problems Which boundary conditions do you know Write a general operator equation and describe what is what Give an example for differential and integral equations Write Maxwell s equations in differential form Describe in details the physics of the Faraday s law Write Maxwell s equations in integral form Describe in details the physics of MaxwellAmpere s law What is a wave equation Why is it important How do we derive it give an example for a source free VWE for the electric eld in linear isotropic homogeneous medium Denote the operator Why do we need boundary conditions BCs How do we classify BCs based on the physics State natural BCs in words and mathematically you do not need to derive those Why do we care about the numerical integration NI What is the basic premises of the NI Describe the Euler s rule Provide all the steps needed for the numerical implementation What do you observe with respect to this method Describe the trapezoidal rule Provide the steps needed for the numerical implementation What do you observe with respect to this method Describe the Simpson s rule Provide the steps needed for the numerical implementation What do you observe with respect to this method Do we know what is the error in this method Describe the Gauss integration Provide the steps needed for the numerical implementation Derive the weights and sampling points for the one point rule Derive the weights and sampling points for the two point Gauss integration rule Which factors determine the accuracy of a numerical method What should we do to improve the accuracy Which types of errors are used in this process What would you do if the exact solution is not known apriori Provide the steps needed to determine the order of convergence Are there any other way for determining the convergence order Why do we care about matrices Which kinds arise in PDE and IE BVPs What is the positive de niteness What are the norms Which errors occur in solving linear systems of equations LSE How do we understandstudy these errors How would you estimate a condition number What could happen if the condition number is high Why is the variation of solution vector high when you have large condition numbers derive mathematically How do we invert system matrix A in Axb Which solvers should we use What do you know about the Gauss elimination do not need to go step by step What are the major difficulties with GE D O N W C UIJB N 000 O W W N W 4 W U What is the LU decomposition conceptually Why is it good What should we do if the elements on the main diagonal are zero aii0 What is a Cholesky decomposition Can you always apply it Is it more ef cient computationally than the LU decomposition Why do we care about iterative methods IM How would you classify IMs Describe the Jacobi s algorithm What are the differences between the Jacobi and GaussSaidel s algorithms What is the preconditioning and why do we care about it For a matrix A determine the diagonal preconditioner Will diagonal preconditioner always help What is a nite difference method FDM What are the steps in FDM Describe in as many details as you can the discretization step Describe the basic premises of the steps settingup FD equations Solve Extraction of parameters For a general lD function derive the forward backward and central nite difference the lowest order Provide a sketch for the function What is the order of accuracy for these approximations and how would you establish that order just say in the words you don t need to derive Derive the lowest order forward difference for the 2 order derivative on a 1D function fx How do we de nederive the nite difference for 2D functions For a 2D Poisson equation provide the basic nite difference equation sketch the arbitrary 2D domain as well FD example similar or the same like we had in the class 7 with 3 nodes in the enclosure Derive the FD equation for a node point on the boundary between two electrically dissimilar media What is accuracy What is stability What are the error sources in FD and how does the round off and discretization errors depend on the sampling size What is the outcomeresult of a FD method How do you compute the capacitance How do you compute the stored energy What about the characteristic impedance What about the phase velocity Effective dielectric constant What is the extraction to the zero grid size Can you use FDM for the eigenvalue problems and if you can how

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