Answer: Ophiopogon japonicus is commonly called Mondo Grass or Dwarf Lilyturf. It's a grass-like evergreen perennial forming clumps of strap-like (1/8" wide) foliage. It spreads via underground runners, is long lived and easily divided. It can also be propagated by seed; each berry (usually produced in autumn) has one seed.
Mondo grass grows best in filtered sun to full shade; requires good drainage, and prefers slightly acidic, humus-rich soil. Divide and prune out brownish foliage in spring before new growth begins. Apply leaf mold in autumn and keep barely moist in winter.
I'd move the grass to a shadier location and find a sun-loving groundcover instead. Consider dichondra, fragaria (ornamental strawberry), Ajuga (carpet bugle) or Arctotheca calendula (Cape Weed) for your sunny yard.
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