NUMERICAL CALCULATIONS IN CLIFFORD ALGEBRA An intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. Applications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of particular types, including scalars, bicomplex numbers, quaternions, Pauli matrices, and extended electromagnetic fields. Readers will find: A thorough introduction to Clifford algebra, with a combination of theory and practical implementation in a range of engineering problems Comprehensive explorations of a variety of worked and computed examples at various levels of complexity Practical discussions of the conceptual and computational tools for solving common engineering problems Detailed documentation on the deployment and application of the Clifford Numerical Suite Perfect for engineers, researchers, and academics with an interest in Clifford algebra, Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists will particularly benefit professionals in the areas of antenna design, digital image processing, theoretical physics, and geometry.

This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green's functions, double integrals, vector calculus and the combined field integral equation (CFIE). Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. The ultimate outcome is an integral formulation that lends itself to a more direct and efficient solution than conventionally is the case, and applies without exception to all types of materials. On any particular machine, it results in either a faster solution for a given problem or the ability to solve problems of greater complexity. The Clifford-Cauchy-Dirac technique offers very real and significant advantages in uniformity, complexity, speed, storage, stability, consistency and accuracy.

This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green's functions, double integrals, vector calculus and the combined field integral equation (CFIE). Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. The ultimate outcome is an integral formulation that lends itself to a more direct and efficient solution than conventionally is the case, and applies without exception to all types of materials. On any particular machine, it results in either a faster solution for a given problem or the ability to solve problems of greater complexity. The Clifford-Cauchy-Dirac technique offers very real and significant advantages in uniformity, complexity, speed, storage, stability, consistency and accuracy.