Download Application of Geometric Algebra to Electromagnetic by Andrew Seagar PDF

By Andrew Seagar

This paintings offers the Clifford-Cauchy-Dirac (CCD) approach for fixing difficulties related to the scattering of electromagnetic radiation from fabrics of all kinds.

It permits a person who's to grasp ideas that bring about less complicated and extra effective strategies to difficulties of electromagnetic scattering than are presently in use. The method is formulated by way of the Cauchy kernel, unmarried integrals, Clifford algebra and a whole-field procedure. this can be unlike many traditional options which are formulated when it comes to Green's features, double integrals, vector calculus and the mixed box critical equation (CFIE). while those traditional concepts result in an implementation utilizing the tactic of moments (MoM), the CCD method is applied as alternating projections onto convex units in a Banach space.

The final end result is an imperative formula that lends itself to a extra direct and effective answer than conventionally is the case, and applies with out exception to every kind of fabrics. On any specific laptop, it leads to both a speedier resolution for a given challenge or the facility to unravel difficulties of larger complexity. The Clifford-Cauchy-Dirac strategy deals very genuine and demanding merits in uniformity, complexity, pace, garage, balance, consistency and accuracy.

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Extra resources for Application of Geometric Algebra to Electromagnetic Scattering: The Clifford-Cauchy-Dirac Technique

Example text

Check your software against question 10. Q18. Implement using a computer language of your choice, software to multiply two arbitrary Clifford numbers using the right inner product. A18. Check your software against question 11. Q19. Implement using a computer language of your choice, software to multiply two arbitrary Clifford numbers using the scalar product. A19. Check your software against question 12. Q20. Implement using a computer language of your choice, software to multiply two arbitrary Clifford numbers using the dot product.

A11. −1 − 1e1 . Q12. Calculate the scalar product (a, b) of the two Clifford numbers a = 2 − 1e1 and b = 1 + 3e1 + 2e2 + 4e1 e2 . A12. −1. Q13. Calculate the dot product a · b of the two Clifford numbers a = 2 − 1e1 and b = 1 + 3e1 + 2e2 + 4e1 e2 . A13. −3. Q14. Implement using a computer language of your choice, software to multiply two arbitrary Clifford numbers using the central product. A14. Check your software against question 7. 5 Exercises 35 Q15. Implement using a computer language of your choice, software to multiply two arbitrary Clifford numbers using the outer product.

The inner product a ∨ b (denoted by the symbol ‘∨’) is constrained to produce non-zero values only when either of the factors e A , e B is composed of units, all of which match any unit in the other. Grassmann called the outer and inner products by those names because they give non-zero results only if the two factors e A , e B either lie completely outside the linear span of the primal units contained in each other, or one lies completely inside the linear span of the primal units contained in the other.

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