“…Moreover solver of UMFPACK was used for solving symmetric problems. Some researchers have asserted the applicability and accuracy of UMFPACK for solving membrane equations (Razavi et al, , 2014Fasihi et al, 2012;Shirazian et al, 2012a,b,c,d,e;Rezakazemi et al, 2013aRezakazemi et al, ,b,c, 2011aRezakazemi et al, ,b, 2012Shirazian and Ashrafizadeh, 2013, 2010a,b, 2014, 2015aFadaei et al, 2011aFadaei et al, ,b, 2012Ghadiri et al, 2013b;Marjani et al, ,b,c, 2011aMarjani and Shirazian, 2010,b,c,d,e, 2012aHemmati et al, 2015;Hoshyargar et al, 2012;Khansary et al, 2015;Kohnehshahri et al, 2011;Moghadassi et al, 2011;Mohammadi et al, 2015;Moradi et al, 2013;Nosratinia et al, 2015;Pishnamazi et al, 2012;Ranjbar et al, 2013;Shirazian et al, 2011aShirazian et al, ,b, 2009Sohrabi et al, 2011a,b,c,d,e;Valavi et al, 2013). Triangular mesh elements used for the evaluation of gas behavior in the HFMC are illustrated in Fig.…”