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The concept of guard rings/points/"halos" is well known in sequential case where one has for a trivial example in one dimension (shown above) 16 points.
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The end points are fixed boundary values
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One could save space and dimension PHI(14) and use boundary values by statements for I=1,14 like
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IF( I.EQ.1) Valueonleft = BOUNDARYLEFT
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ELSE Valueonleft = PHI(I-1) etc.
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But this is slower and clumsy to program due to conditionals INSIDE Loop and one dimensions instead PHI(16) storing boundary values in PHI(1) and PHI(16)
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Updates are performed as DO I =2,15
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and without any test Valueonleft = PHI(I-1)
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