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An efficient VLSI algorithm for solving the model biharmonic problem will be presented. The complexity of this VLSI solver will be characterized in terms of the area $\times$ time measure $A{T^2}$, where $A$ and $T$ stand respectively for the {\it time} and the {\it area} required for the parallel algorithm.
The first boundary value problem for the biharmonic equation will be considered for a rectangular domain with $n\times n$ interior grid points. The VLSI algorithm is based on the semidirect approach which treats the biharmonic operator as a coupled pair of Laplace operators.
The design is of a compact form where one VLSI block performs all operations of the semidirect cycle. Its length and height are proportional to $O(n{ \log n}) $. The total parallel computational time is $O(\sqrt{n}{ \log}^2n)$. Hence, the global estimation in $A{T^2}$ complexity measure is $O({n^3}{{ \log}^6n})$ for this algorithm. This represents the best $A{T^2}$ upper bound for the biharmonic problem until now.
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