World number one Tiger Woods has been drawn to play alongside Graeme McDowell and South African Louis Oosthuizen in the first two rounds of this week's Open Championship at Muirfield.

The trio will tee-off at 2:45pm on Thursday and at 9:44 on Friday.

Second-ranked Rory McIlroy has been grouped with American left-hander Phil Mickelson, last week's Scottish Open winner, and Japan's Hideki Matsuyama.

Shane Lowry will be among the first out on course on Thursday with a 7:49am tee-time as he plays alongside Ben Curtis of the US and Spain's Rafael Cabrera-Bello.

Padraig Harrington has a leisurely 1:01pm start and he will play with Michael Thompson of the US and Scotland's Richie Ramsay, while Darren Clarke, Vijay Singh and Martin Laird will immediately follow them.

Woods, who will be making his first competitive appearance since last month's US Open in Pennsylvania, played nine holes in practice on Sunday.

The 14-times major winner said he still needed medication and treatment on his injured left elbow.

He had been suffering with minor discomfort ahead of the U.S. Open at Merion where he aggravated the problem and was seen wincing and shaking his arm on several occasions.

"I started chipping and putting a little over a week ago and I'm full go for the British Open," the 37-year-old American said on his website ( on Saturday.

"I'm very confident my elbow strain won't be a problem and I will be able to hit all the shots I need to hit.

"The big thing at Muirfield will be to avoid the rough," added Woods. "Although I have been playing every day I also have to get back into a competitive feel."

Woods is making his second appearance at a Muirfield-hosted British Open after finishing tied 28th in 2002.

"My first visit didn't go very well. I caught the worst of the weather," he said.

"That's just the nature of links golf. Luck plays a big part in it and you never know what you're going to get."

World number seven McDowell is one of golf's hottest players this year, having won the World Match Play Championship in Bulgaria, the RBC Heritage in South Carolina and this month's French Open in Versailles.

Oosthuizen won the British Open, golf's oldest major, at St Andrews in 2010.

Title holder Ernie Els, U.S. Open winner Justin Rose and American Brandt Snedeker feature in another marquee three-ball at 0911 in Thursday's opening round at Muirfield.

US Masters champion Adam Scott has been drawn to play with American Matt Kuchar and Britain's Luke Donald at 1412.

Lee Westwood and Sergio Garcia play alongside former U.S. Masters champion Charl Schwartzel of South Africa while the fans will be squinting into the distance if they choose to follow the big-hitting group of Belgian Nicolas Colsaerts and U.S. Ryder Cup duo Dustin Johnson and Bubba Watson.