The current trend of computer architecture evolving towards exaflop/s is the fast increasing floating point performance (the so-called �free� flops) accompanied by much slowly improving the bandwidth of memory and network. Numerical simulation would undergo the challenge posed by the unbalanced increase in the compute power and the capability of data movement. In this paper, after reviewing the challenges of hardware and software in moving towards exascale computing, we present co-design thinking for selecting, optimizing, and developing a numerical algorithm and a simulation tool to meet the challenge of simulation at extreme scale. Examples are presented to demonstrate the new way of thinking and its effectiveness on the emerging architecture.
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