Efficient Implementation of Multilevel Fast Multipole Algorithm via Fourier Series for One-Dimensional Problems
In the past few decades, computational simulation has become an accepted paradigm for scientific discovery, especially with the dramatic growth in fast computers and powerful software. Generally, simulations involve several million variables. Most large problems boil down to the solution of a linear system or performing a matrix-vector product. Regular product requires O(NxN) time and O(NxN) memory. The Multilevel Fast Multipole Method (MLFMM), which has been acclaimed as one of the most efficient algorithms of the 20th century, dramatically reduces the complexity of matrix-vector multiplication involving a certain type of dense matrix, which can arise out of many physical systems. MLFMM achieves this product in O(N log N) time and memory.
In this algorithm, the Green’s function is approximated by an expression that separates the receiver point from the source point. Each problem has a unique Green’s function which means derivations are required to get the approximation. As a result, each problem requires a new code even though the algorithm is the same for all problems. To solve these issues, the MLFMA is executed by approximate the Green’s function by a Fourier series. The proposed approach is straightforward approach to find the approximation. Also, the code will be the same whatever the problem is going to be. Scattering of the electromagnetic wave from one-dimensional perfect electric conductor surfaces is solved using the proposed approach and the conventional approach. The results revealed that the suggested method is precise and faster than the conventional approach.
Dr. Mohammad Ahmad holds a Ph.D. in Electrical Engineering from the University of Massachusetts, USA, specializing in Electromagnetics, Propagation of Waves. His academic journey began with a bachelor’s degree in communication and Electronics Engineering from Applied Science University, Jordan, followed by a master’s degree in communication engineering from the University of Jordan, Jordan.
With a passion for research and teaching, Dr. Ahmad has dedicated himself to academia for several years. He served as an assistant professor at Zarqa University, Jordan, for two years before transitioning to Applied Science University/ London South Bank University, Bahrain, where he continued his role as an assistant professor and course director for another two years.
Throughout his academic career, Dr. Ahmad has contributed significantly to the fields of Electromagnetics and Propagation of Waves. His research interests lie at the intersection of technology and innovation, exploring the application of cutting-edge concepts to solve real-world problems. Dr. Ahmad has pioneered innovative solutions in electromagnetics, boldly venturing beyond traditional methodologies to harness the power of neural networks in solving complex electromagnetic problems. His groundbreaking work not only transcends conventional approaches but also opens new frontiers in the realm of artificial intelligence applications in electromagnetics and wave propagation. As Dr. Ahmad continues to push the boundaries of research, his focus remains steadfast on leveraging cutting-edge artificial intelligence techniques to unravel the mysteries of electromagnetic phenomena and advance the field to unprecedented heights.
Driven by a commitment to academic excellence and a thirst for knowledge, Dr. Mohammad Ahmad continues to inspire and educate future generations of engineers and researchers, leaving an indelible mark on the landscape of electrical engineering and beyond.