五代數(shù)方程的求解-資料下載頁
2025-07-17 12:48本頁面
【正文】 ???????????????????網(wǎng)格上的誤差方程差比較光滑，可以在粗當(dāng)收斂較慢時(shí)，表明殘細(xì)網(wǎng)格上殘差誤差方程細(xì)網(wǎng)格上需解方程：39 限制和插值算子 : 對于 eq () 1/2*eq(i1)+ 189。*eq(i+1) +eq(i) results in: 40 Comparison of count for convergence ? On 2D Poisson equation, k*k grid, n=k2, unknown Method Cost Gaussian elimination O(n3) GS O(n2logn) CG O() FFT/Cyclic reduction O(nlogn) Multigrid O(n) optimal 41 選擇 solver ? MG+SIP or MG +GS ICCG SIP ADI GS ? GMRES+MG ? 沒有 MG時(shí)， ICCGSIP ADI GS 42 其他迭代法 coupled equations (system of nonlinear equations) ? Simultaneous approach: All equations are considered part of a single system. ? Sequential approach: Each equation is solved for its dominant variable, treating the other as known, and one iterates through the equations until the solution of the coupled system is obtained. ? Iterations performed on each equation are called inner iteration. ? In order to obtain a solution which satisfy all equations, the coefficient matrices and source vector must be updated after each cycle ad the process repeated. The cycle are called outer iteration. 43 Sequential solution: UnderRelaxation On the nth iteration the equation for generic variable is Patankar 1980對 SIMPLE采用 , 穩(wěn)定求解，但可能降低收斂率 時(shí)間相關(guān)法就是一種松馳法。 44 deferredcorrection approaches 對于高階差分離散，如果左端項(xiàng)用高階差分 ,則計(jì)算復(fù)雜 如果左端項(xiàng)只保留相鄰點(diǎn)的項(xiàng)，遠(yuǎn)鄰點(diǎn)移到右端，則計(jì)算可能發(fā)散 為克服上述困難，可用延遲修正 : 高階差分移到右端，同時(shí)在左右兩端加僅涉及相鄰點(diǎn)的低階差分： 用途：可以處理隱式高階差分、交叉導(dǎo)數(shù)項(xiàng)、非正交相等。但不能處理高階導(dǎo)數(shù)項(xiàng)。 45 第 5次課閱讀提示 ? 傅 《 計(jì)算流體力學(xué) 》 第 5章全部。 ? Peric《 書 》 Chapter 5 全部。 46 第五次課后作業(yè) ? 實(shí)踐 Peric《 書 》 附的代數(shù)方程求解程序 ? （待具體 化）
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