M$8$ How does the implementation of advanced numerical methods, such as the finite element method $($FEM$),$ influence the precision and reliability of structural analysis in civil engineering, particularly in the context of complex loading conditions and material non$-$linearities, and what are the implications of these advanced computational techniques for the design, safety, and cost$-$effectiveness of large$-$scale infrastructure projects, considering both current limitations and potential future advancements in computational power and algorithm development?