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In a recent invited paper in the IEEE Antennas and Propagation Magazine, some of the challenging problems in computational electromagnetics were presented. One of the objectives of this note is to simply point out that challenging to one may be simple to another. This is demonstrated through an example cited in that article. The example chosen is a Vivaldi antenna array. What we discuss here also applies to the other examples presented in that article, but we have chosen the Vivaldi antenna array to help us make our point. It is shown in this short article that a higher-order basis using a surface integral equation a la a PMCHWT (Poggio-Miller-Chu-Harrington-Wu-Tsai) method-of-moments formulation may still be the best weapon that one have in today's arsenal to deal with challenging complex electromagnetic analysis problems. Here, we have used the commercially available code WIPL-D to carry out all the computations using laptop/desktop systems. The second objective of this paper is to present an out-of-core solver. The goal is to demonstrate that an out-of-core 32-bit-system-based solver can be as efficient as a 64-bit in-core solver. This is quite contrary to the popular belief that an out-of-core solver is generally much slower than an in-core solver. This can be significant, as the difference in the cost of a 32-bit system can be 1/30 of a 64-bit system of similar capabilities using current computer architectures. For the 32-bit system, we consider a Pentium 4 system, whereas for the 64-bit system, we consider an Itanium 2 system for comparison. The out-of-core solver can go beyond the 2 GB limitation for a 32-bit system and can be run on ordinary laptop/desktop; hence, we can simultaneously have a much lower hardware investment while better performance for a sophisticated and powerful electromagnetic solver. The system resources and the CPU times are also outlined.