Amina Al-Jeffery, 21, from Swansea, who has dual British and Saudi Arabian nationality, claims Mohammed Al-Jeffery locked her up after she "kissed a guy".
Her lawyers have taken legal action in London in a bid to protect her but her father has denied the claims.
The judge said a ruling on the case would be issued in public.
Barristers Henry Setright QC and Michael Gration, representing Miss Al-Jeffery, have asked Mr Justice Holman to look at ways of coming to her aid.
The judge has been analysing the case in the Family Division of the High Court in London and the hearing ended late on Thursday.
Lawyers are due to file final documentation on Monday and Mr Justice Holman is scheduled to deliver a ruling on Wednesday.
Mr Justice Holman has said there are reasons to be very concerned about Miss Al-Jeffery's welfare.
And he rejected an application from Mr Al-Jeffery for restrictions to be placed on what journalists can report.
The judge has been told Miss Al-Jeffery left Swansea and moved to Saudi Arabia at her father's insistence four years ago.
He has heard that Miss Al-Jeffery's mother and siblings are back in south Wales.
Neither Miss Al-Jeffery nor her father, an academic who is in his 60s, have been at the court hearing.
Barrister Marcus Scott-Manderson QC, representing Mr Al-Jeffery, told Mr Justice Holman at the end of proceedings on Thursday that Mr Al-Jeffery wanted "reporting restrictions".
But Mr Justice Holman said: "No. Afraid not."
He said there were good reasons for staging the hearing in public - even though it was in a family court - and allowing journalists to report freely.
Mr Justice Holman said the case involved the welfare of an adult who was a British citizen.
"I happen to think that the case raises issues that require to be ventilated in public," said the judge.
"I dare say the publicity is extremely disagreeable to the father."
A father accused of imprisoning his daughter at their home in Saudi Arabia has failed in a bid to limit reporting of the case.