Steffen Börm said in New $H^{2}$-matrix algorithm:

I have spent a large amount of time looking for efficient algorithms for $H^2$-matrix arithmetics that can handle fairly general block structures. Following the H-matrix paradigm, the starting point is the multiplication of $H^2$-matrices.

After several years of disappointing results, the newest algorithm finally seems to be sufficiently fast. Let’s see if a similar approach can be found for the LU factorization.

From above I can see that even for the best luminary in the BEM research area, he has still spent several years with disappointing results to finally achieve an efficient and usable algorithm. It can be envisioned that how much efforts and lucubration are involved during this process. Hence, there is no reason for me to crave quick or efficient success anymore, even though it is fascinating. What I’m only aware of and concerned about are the following points:

  1. whether I’m working work hard enough,
  2. whether I have reviewed, reorganized and practiced learned theories and
  3. whether I have mastered necessary engineering crafts, such as programming techniques.

The trick here is that the less I desire something, the quicker I get close to it.